Finite Group Databasebeta

← C73×#14520 #32923924

Subgroups — C73×#14520 #32923924

Order 18688.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C73C211yesmaximal, characteristic
2C2×#390×C73C211yesmaximal, characteristic, complemented
3C2×#388×C73C211yesmaximal, characteristic, complemented
4C2×#386×C73C211yesmaximal, characteristic, complemented
5C2×#386×C73C211yesmaximal, characteristic, complemented
6C73×#1442C211yesmaximal, characteristic, complemented
7C73×#1440C211yesmaximal, characteristic, complemented
8C73×#1438C211yesmaximal, characteristic, complemented
9C73×#1438C211yesmaximal, characteristic, complemented
10C73×#1438C211yesmaximal, characteristic, complemented
11C73×#1437C211yesmaximal, characteristic, complemented
12C73×#1437C211yesmaximal, characteristic, complemented
13C73×#1437C211yesmaximal, characteristic, complemented
14C73×#1434C211yesmaximal, characteristic, complemented
15C73×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C23×D4×C73C2211yescharacteristic
19C24×C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C22⋊C4×C73C2211yescharacteristic
22C22×C22⋊C4×C73C2211yescharacteristic
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C22×C22⋊C4×C73C2211yescharacteristic
33C22×C22⋊C4×C73C2211yescharacteristic
34C22×C22⋊C4×C73C2211yescharacteristic
35C22×C42×C73C2211yescharacteristic
36C22×C42×C73C2211yescharacteristic
37#392×C73C418yescomplemented
38#390×C73—24no—
39#388×C73—24no—
40#386×C73—24no—
41#386×C73—24no—
42C2×#95×C73C2211yescharacteristic
43C2×#95×C73C2211yescharacteristic
44C2×#95×C73C2211yescharacteristic
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C25×C73C2311yescharacteristic
57C25×C73C2311yescharacteristic
58C25×C73C2311yescharacteristic
59C22×D4×C73—22no—
60C22×D4×C73—22no—
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—41no—
66C22×D4×C73—41no—
67C22×D4×C73—41no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73—41no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73—41no—
76C22×D4×C73—41no—
77C22×D4×C73C2×C414yes—
78C22×D4×C73C2×C414yes—
79C22×D4×C73C2×C414yescomplemented
80C23×C4×C73—22no—
81C23×C4×C73—22no—
82C23×C4×C73—22no—
83C23×C4×C73—41no—
84C23×C4×C73—41no—
85C23×C4×C73—41no—
86C23×C4×C73—41no—
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C23×C4×C73C2311yescharacteristic
93C23×C4×C73C2311yescharacteristic
94C23×C4×C73C2311yescharacteristic
95C23×C4×C73C2311yescharacteristic
96C23×C4×C73C2311yescharacteristic
97C23×C4×C73C2311yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73—22no—
100C2×C4⋊C4×C73—22no—
101C2×C4⋊C4×C73—41no—
102C2×C22⋊C4×C73—22no—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73—22no—
105C2×C22⋊C4×C73—22no—
106C2×C22⋊C4×C73—22no—
107C2×C22⋊C4×C73—22no—
108C2×C22⋊C4×C73—22no—
109C2×C22⋊C4×C73—22no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—22no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—22no—
119C2×C22⋊C4×C73—22no—
120C2×C22⋊C4×C73—41no—
121C2×C22⋊C4×C73—41no—
122C2×C22⋊C4×C73—41no—
123C2×C22⋊C4×C73—41no—
124C2×C22⋊C4×C73—41no—
125C2×C22⋊C4×C73—41no—
126C2×C22⋊C4×C73—41no—
127C2×C22⋊C4×C73—41no—
128C2×C22⋊C4×C73—41no—
129C2×C22⋊C4×C73—41no—
130C2×C22⋊C4×C73—41no—
131C2×C22⋊C4×C73—41no—
132C2×C22⋊C4×C73—41no—
133C2×C22⋊C4×C73—41no—
134C2×C22⋊C4×C73—41no—
135C2×C22⋊C4×C73—41no—
136C2×C22⋊C4×C73—41no—
137C2×C22⋊C4×C73—41no—
138C2×C22⋊C4×C73—41no—
139C2×C22⋊C4×C73—41no—
140C2×C22⋊C4×C73C2×C414yes—
141C2×C22⋊C4×C73C2×C414yescomplemented
142C2×C22⋊C4×C73C2×C414yescomplemented
143C2×C22⋊C4×C73D414yescomplemented
144C2×C42×C73—22no—
145C2×C42×C73—22no—
146C2×C42×C73—22no—
147C2×C42×C73—41no—
148C2×C42×C73—41no—
149C2×C42×C73—41no—
150#95×C73—22no—
151#95×C73—22no—
152#95×C73—22no—
153#95×C73—22no—
154#95×C73—41no—
155#95×C73—41no—
156#95×C73—41no—
157#95×C73—41no—
158#95×C73—41no—
159#95×C73—41no—
160#95×C73—41no—
161#95×C73—41no—
162#95×C73C2×C414yescomplemented
163#95×C73D414yescomplemented
164C24×C73—21no—
165C24×C73—21no—
166C24×C73—21no—
167C24×C73—21no—
168C24×C73—21no—
169C24×C73—21no—
170C24×C73—21no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—21no—
174C24×C73—21no—
175C24×C73—21no—
176C24×C73—21no—
177C24×C73—21no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—21no—
181C24×C73—21no—
182C24×C73—21no—
183C24×C73—21no—
184C24×C73—21no—
185C24×C73—21no—
186C24×C73—21no—
187C24×C73—21no—
188C24×C73—21no—
189C24×C73—21no—
190C24×C73—21no—
191C24×C73—21no—
192C24×C73—21no—
193C24×C73—21no—
194C24×C73—21no—
195C24×C73—21no—
196C24×C73—21no—
197C24×C73—21no—
198C24×C73—21no—
199C24×C73—21no—
200C24×C73—21no—
201C24×C73—21no—
202C24×C73—21no—
203C24×C73—21no—
204C24×C73C22×C412yes—
205C24×C73C22×C412yes—
206C24×C73C22×C412yes—
207C24×C73C2×D412yes—
208C24×C73#4112yes—
209C24×C73C2411yescharacteristic
210C2×D4×C73—28no—
211C2×D4×C73—28no—
212C2×D4×C73—28no—
213C2×D4×C73—44no—
214C2×D4×C73—44no—
215C2×D4×C73—44no—
216C2×D4×C73—44no—
217C2×D4×C73—44no—
218C2×D4×C73—44no—
219C2×D4×C73—44no—
220C2×D4×C73—44no—
221C2×D4×C73—44no—
222C2×D4×C73—44no—
223C2×D4×C73—44no—
224C2×D4×C73—44no—
225C2×D4×C73—44no—
226C2×D4×C73—44no—
227C2×D4×C73—44no—
228C2×D4×C73—44no—
229C2×D4×C73—44no—
230C2×D4×C73—44no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73—21no—
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73—21no—
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73—21no—
279C22×C4×C73—21no—
280C22×C4×C73—21no—
281C22×C4×C73—21no—
282C22×C4×C73—21no—
283C22×C4×C73—21no—
284C22×C4×C73—21no—
285C22×C4×C73—21no—
286C22×C4×C73—21no—
287C22×C4×C73—21no—
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—21no—
297C22×C4×C73—21no—
298C22×C4×C73—21no—
299C22×C4×C73—21no—
300C22×C4×C73—21no—
301C22×C4×C73—21no—
302C22×C4×C73—21no—
303C22×C4×C73—44no—
304C22×C4×C73—44no—
305C22×C4×C73—44no—
306C22×C4×C73—44no—
307C22×C4×C73—44no—
308C22×C4×C73—44no—
309C22×C4×C73—44no—
310C22×C4×C73C22×C412yes—
311C22×C4×C73C22×C412yes—
312C22×C4×C73C22×C412yes—
313C22×C4×C73C22×C412yes—
314C22×C4×C73C2×D412yes—
315C22×C4×C73C2×D412yes—
316C22×C4×C73C2×D412yes—
317C22×C4×C73C2×D412yes—
318C22×C4×C73C2×D412yes—
319C22×C4×C73#4112yes—
320C22×C4×C73#4112yes—
321C22×C4×C73#4112yes—
322C4⋊C4×C73—44no—
323C22⋊C4×C73—28no—
324C22⋊C4×C73—44no—
325C22⋊C4×C73—44no—
326C22⋊C4×C73—44no—
327C22⋊C4×C73—44no—
328C22⋊C4×C73—44no—
329C22⋊C4×C73—44no—
330C22⋊C4×C73—44no—
331C22⋊C4×C73—44no—
332C22⋊C4×C73—44no—
333C22⋊C4×C73—44no—
334C22⋊C4×C73—44no—
335C22⋊C4×C73—44no—
336C22⋊C4×C73—44no—
337C42×C73—44no—
338C42×C73—44no—
339C23×C73—22no—
340C23×C73—22no—
341C23×C73—22no—
342C23×C73—22no—
343C23×C73—22no—
344C23×C73—22no—
345C23×C73—22no—
346C23×C73—22no—
347C23×C73—22no—
348C23×C73—22no—
349C23×C73—22no—
350C23×C73—22no—
351C23×C73—22no—
352C23×C73—22no—
353C23×C73—22no—
354C23×C73—22no—
355C23×C73—22no—
356C23×C73—22no—
357C23×C73—22no—
358C23×C73—22no—
359C23×C73—22no—
360C23×C73—22no—
361C23×C73—22no—
362C23×C73—22no—
363C23×C73—22no—
364C23×C73—22no—
365C23×C73—22no—
366C23×C73—22no—
367C23×C73—22no—
368C23×C73—22no—
369C23×C73—22no—
370C23×C73—22no—
371C23×C73—41no—
372C23×C73—41no—
373C23×C73—41no—
374C23×C73—41no—
375C23×C73—41no—
376C23×C73—41no—
377C23×C73—41no—
378C23×C73—41no—
379C23×C73—41no—
380C23×C73—41no—
381C23×C73—41no—
382C23×C73—41no—
383C23×C73—41no—
384C23×C73—41no—
385C23×C73—41no—
386C23×C73—41no—
387C23×C73—41no—
388C23×C73—41no—
389C23×C73—41no—
390C23×C73—41no—
391C23×C73—41no—
392C23×C73—41no—
393C23×C73—41no—
394C23×C73—41no—
395C23×C73—41no—
396C23×C73—41no—
397C23×C73—41no—
398C23×C73—41no—
399C23×C73—41no—
400C23×C73—41no—
401C23×C73—41no—
402C23×C73—41no—
403C23×C73—41no—
404C23×C73—41no—
405C23×C73—41no—
406C23×C73—41no—
407C23×C73—41no—
408C23×C73—41no—
409C23×C73—41no—
410C23×C73—41no—
411C23×C73—41no—
412C23×C73—41no—
413C23×C73—41no—
414C23×C73—41no—
415C23×C73—41no—
416C23×C73—41no—
417C23×C73—41no—
418C23×C73—41no—
419C23×C73—41no—
420C23×C73—41no—
421C23×C73—41no—
422C23×C73—41no—
423C23×C73—41no—
424C23×C73—41no—
425C23×C73—41no—
426C23×C73—41no—
427C23×C73—41no—
428C23×C73—41no—
429C23×C73—41no—
430C23×C73—41no—
431C23×C73—41no—
432C23×C73—41no—
433C23×C73—41no—
434C23×C73—41no—
435C23×C73—41no—
436C23×C73—41no—
437C23×C73—41no—
438C23×C73—41no—
439C23×C73—41no—
440C23×C73—41no—
441C23×C73—41no—
442C23×C73—41no—
443C23×C73C4×D414yes—
444C23×C73C23×C411yescharacteristic
445C23×C73C22×D411yescharacteristic
446C23×C73C22×D411yescharacteristic
447C23×C73C2×#4111yescharacteristic
448C23×C73C2×#4111yescharacteristic
449C23×C73C2×#4111yescharacteristic
450C23×C73C2×#4111yescharacteristic
451C23×C73H(5,𝔽2)11yescharacteristic
452C23×C73H(5,𝔽2)11yescharacteristic
453C23×C73H(5,𝔽2)11yescharacteristic
454C23×C73H(5,𝔽2)11yescharacteristic
455C23×C73H(5,𝔽2)11yescharacteristic
456C23×C73H(5,𝔽2)11yescharacteristic
457C23×C73H(5,𝔽2)11yescharacteristic
458C23×C73H(5,𝔽2)11yescharacteristic
459D4×C73—416no—
460D4×C73—416no—
461D4×C73—416no—
462C2×C4×C73—22no—
463C2×C4×C73—22no—
464C2×C4×C73—22no—
465C2×C4×C73—22no—
466C2×C4×C73—22no—
467C2×C4×C73—22no—
468C2×C4×C73—22no—
469C2×C4×C73—22no—
470C2×C4×C73—22no—
471C2×C4×C73—22no—
472C2×C4×C73—22no—
473C2×C4×C73—22no—
474C2×C4×C73—22no—
475C2×C4×C73—22no—
476C2×C4×C73—22no—
477C2×C4×C73—22no—
478C2×C4×C73—22no—
479C2×C4×C73—22no—
480C2×C4×C73—22no—
481C2×C4×C73—22no—
482C2×C4×C73—22no—
483C2×C4×C73—22no—
484C2×C4×C73—22no—
485C2×C4×C73—22no—
486C2×C4×C73—22no—
487C2×C4×C73—22no—
488C2×C4×C73—22no—
489C2×C4×C73—22no—
490C2×C4×C73—22no—
491C2×C4×C73—22no—
492C2×C4×C73—22no—
493C2×C4×C73—22no—
494C2×C4×C73—22no—
495C2×C4×C73—416no—
496C2×C4×C73—41no—
497C2×C4×C73—41no—
498C2×C4×C73—41no—
499C2×C4×C73—41no—
500C2×C4×C73—41no—
501C2×C4×C73—41no—
502C2×C4×C73—41no—
503C2×C4×C73—41no—
504C2×C4×C73—41no—
505C2×C4×C73—41no—
506C2×C4×C73—41no—
507C2×C4×C73—41no—
508C2×C4×C73—41no—
509C2×C4×C73—41no—
510C2×C4×C73—41no—
511C2×C4×C73—41no—
512C2×C4×C73—41no—
513C2×C4×C73—41no—
514C2×C4×C73—41no—
515C2×C4×C73—41no—
516C2×C4×C73—41no—
517C2×C4×C73—41no—
518C2×C4×C73—41no—
519C2×C4×C73—41no—
520C2×C4×C73—41no—
521C2×C4×C73—41no—
522C2×C4×C73—41no—
523C2×C4×C73—41no—
524C2×C4×C73—41no—
525C2×C4×C73—41no—
526C2×C4×C73—41no—
527C2×C4×C73—41no—
528C2×C4×C73—41no—
529C2×C4×C73—41no—
530C2×C4×C73—41no—
531C2×C4×C73—41no—
532C2×C4×C73—41no—
533C2×C4×C73—41no—
534C2×C4×C73—41no—
535C2×C4×C73—41no—
536C2×C4×C73—41no—
537C2×C4×C73—41no—
538C2×C4×C73—41no—
539C2×C4×C73—41no—
540C2×C4×C73—41no—
541C2×C4×C73—41no—
542C2×C4×C73—41no—
543C2×C4×C73—41no—
544C2×C4×C73—41no—
545C2×C4×C73—41no—
546C2×C4×C73C4×D414yes—
547C22×C73—24no—
548C22×C73—24no—
549C22×C73—24no—
550C22×C73—42no—
551C22×C73—42no—
552C22×C73—42no—
553C22×C73—42no—
554C22×C73—42no—
555C22×C73—42no—
556C22×C73—42no—
557C22×C73—42no—
558C22×C73—42no—
559C22×C73—42no—
560C22×C73—42no—
561C22×C73—42no—
562C22×C73—42no—
563C22×C73—42no—
564C22×C73—42no—
565C22×C73—42no—
566C22×C73—42no—
567C22×C73—42no—
568C22×C73—42no—
569C22×C73—42no—
570C22×C73—42no—
571C22×C73—42no—
572C22×C73—42no—
573C22×C73—42no—
574C22×C73—42no—
575C22×C73—42no—
576C22×C73—81no—
577C22×C73—81no—
578C22×C73—81no—
579C22×C73—81no—
580C22×C73—81no—
581C22×C73—81no—
582C22×C73—81no—
583C22×C73—81no—
584C22×C73—81no—
585C22×C73—81no—
586C22×C73—81no—
587C22×C73—81no—
588C22×C73—81no—
589C22×C73—81no—
590C22×C73—81no—
591C22×C73—81no—
592C22×C73C2×C4×D411yescharacteristic
593C22×C73C2×C4×D411yescharacteristic
594C22×C73C4×#4111yescharacteristic
595C22×C73#51811yescharacteristic
596C22×C73#51811yescharacteristic
597C22×C73#51811yescharacteristic
598C22×C73#51811yescharacteristic
599C22×C73#53411yescharacteristic
600C22×C73#53511yescharacteristic
601C22×C73#53511yescharacteristic
602C22×C73#53511yescharacteristic
603C22×C73#53811yescharacteristic
604C22×C73#53811yescharacteristic
605C22×C73#53811yescharacteristic
606C22×C73#53811yescharacteristic
607C22×C73#54011yescharacteristic
608C22×C73#54011yescharacteristic
609C22×C73#54011yescharacteristic
610C22×C73#54011yescharacteristic
611C22×C73D4211yescharacteristic
612C22×C73#54611yescharacteristic
613C22×C73#54611yescharacteristic
614C22×C73#54611yescharacteristic
615C22×C73#54611yescharacteristic
616C22×C73#54611yescharacteristic
617C22×C73#55011yescharacteristic
618C22×C73#55111yescharacteristic
619C22×C73#55311yescharacteristic
620C22×C73#55311yescharacteristic
621C22×C73#55311yescharacteristic
622C22×C73#55511yescharacteristic
623C22×C73#56011yescharacteristic
624C22×C73#56011yescharacteristic
625C22×C73#56011yescharacteristic
626C22×C73H(3,𝔽4)11yescharacteristic
627C4×C73—24no—
628C4×C73—42no—
629C4×C73—42no—
630C4×C73—42no—
631C4×C73—42no—
632C4×C73—42no—
633C4×C73—42no—
634C4×C73—42no—
635C4×C73—42no—
636C4×C73—42no—
637C4×C73—81no—
638C4×C73—81no—
639#14520C7311yesmaximal, characteristic, direct product factor, Sylow
640C2×C73—44no—
641C2×C73—82no—
642C2×C73—82no—
643C2×C73#232111yescharacteristic
644C2×C73#232811yescharacteristic
645C2×C73#233311yescharacteristic
646C2×C73#235811yescharacteristic
647C2×C73#236311yescharacteristic
648C2×C73#236411yescharacteristic
649C2×C73#237511yescharacteristic
650C2×C73#267011yescharacteristic
651C2×C73#267311yescharacteristic
652C2×C73#269911yescharacteristic
653C2×C73#270311yescharacteristic
654C2×C73#270311yescharacteristic
655C2×C73#271411yescharacteristic
656C2×C73#275311yescharacteristic
657C2×C73#275611yescharacteristic
658C2×#392C2×C7311yescharacteristic
659C2×#390C2×C7311yescharacteristic, complemented
660C2×#388C2×C7311yescharacteristic, complemented
661C2×#386C2×C7311yescharacteristic, complemented
662C2×#386C2×C7311yescharacteristic, complemented
663#1442C2×C7311yescharacteristic, complemented
664#1440C2×C7311yescharacteristic, complemented
665#1438C2×C7311yescharacteristic, complemented
666#1438C2×C7311yescharacteristic, complemented
667#1438C2×C7311yescharacteristic, complemented
668#1437C2×C7311yescharacteristic, complemented
669#1437C2×C7311yescharacteristic, complemented
670#1437C2×C7311yescharacteristic, complemented
671#1434C2×C7311yescharacteristic, complemented
672C22⋊#95C2×C7311yescharacteristic, complemented
673C73#1452011yescharacteristic, direct product factor, Sylow
674C23×D4C22×C7311yescharacteristic
675C23×D4C22×C7311yescharacteristic
676C23×D4C22×C7311yescharacteristic
677C24×C4C22×C7311yescharacteristic
678C22×C4⋊C4C22×C7311yescharacteristic
679C22×C22⋊C4C22×C7311yescharacteristic
680C22×C22⋊C4C22×C7311yescharacteristic
681C22×C22⋊C4C22×C7311yescharacteristic
682C22×C22⋊C4C22×C7311yescharacteristic
683C22×C22⋊C4C22×C7311yescharacteristic
684C22×C22⋊C4C22×C7311yescharacteristic
685C22×C22⋊C4C22×C7311yescharacteristic
686C22×C22⋊C4C22×C7311yescharacteristic
687C22×C22⋊C4C22×C7311yescharacteristic
688C22×C22⋊C4C22×C7311yescharacteristic
689C22×C22⋊C4C22×C7311yescharacteristic
690C22×C22⋊C4C22×C7311yescharacteristic
691C22×C22⋊C4C22×C7311yescharacteristic
692C22×C22⋊C4C22×C7311yescharacteristic
693C22×C42C22×C7311yescharacteristic
694C22×C42C22×C7311yescharacteristic
695#392C4×C7318yescomplemented
696#390—24no—
697#388—24no—
698#386—24no—
699#386—24no—
700C2×#95C22×C7311yescharacteristic
701C2×#95C22×C7311yescharacteristic
702C2×#95C22×C7311yescharacteristic
703C2×#95C22×C7311yescharacteristic
704C2×#95C22×C7311yescharacteristic
705C2×#95C22×C7311yescharacteristic
706C2×#95C22×C7311yescharacteristic
707C2×#95C22×C7311yescharacteristic
708C2×#95C22×C7311yescharacteristic
709C2×#95C22×C7311yescharacteristic
710C2×#95C22×C7311yescharacteristic
711C2×#95C22×C7311yescharacteristic
712C2×#95C22×C7311yescharacteristic
713C2×#95C22×C7311yescharacteristic
714C25C23×C7311yescharacteristic
715C25C23×C7311yescharacteristic
716C25C23×C7311yescharacteristic
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4C2×C4×C7314yes—
736C22×D4C2×C4×C7314yes—
737C22×D4C2×C4×C7314yescomplemented
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4C23×C7311yescharacteristic
746C23×C4C23×C7311yescharacteristic
747C23×C4C23×C7311yescharacteristic
748C23×C4C23×C7311yescharacteristic
749C23×C4C23×C7311yescharacteristic
750C23×C4C23×C7311yescharacteristic
751C23×C4C23×C7311yescharacteristic
752C23×C4C23×C7311yescharacteristic
753C23×C4C23×C7311yescharacteristic
754C23×C4C23×C7311yescharacteristic
755C23×C4C23×C7311yescharacteristic
756C23×C4C23×C7311yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—41no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4C2×C4×C7314yes—
799C2×C22⋊C4C2×C4×C7314yescomplemented
800C2×C22⋊C4C2×C4×C7314yescomplemented
801C2×C22⋊C4D4×C7314yescomplemented
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—22no—
805C2×C42—41no—
806C2×C42—41no—
807C2×C42—41no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95—41no—
820#95C2×C4×C7314yescomplemented
821#95D4×C7314yescomplemented
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24C22×C4×C7312yes—
863C24C22×C4×C7312yes—
864C24C22×C4×C7312yes—
865C24C2×D4×C7312yes—
866C24#41×C7312yes—
867C24C24×C7311yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C7312yes—
969C22×C4C22×C4×C7312yes—
970C22×C4C22×C4×C7312yes—
971C22×C4C22×C4×C7312yes—
972C22×C4C2×D4×C7312yes—
973C22×C4C2×D4×C7312yes—
974C22×C4C2×D4×C7312yes—
975C22×C4C2×D4×C7312yes—
976C22×C4C2×D4×C7312yes—
977C22×C4#41×C7312yes—
978C22×C4#41×C7312yes—
979C22×C4#41×C7312yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C42—44no—
996C42—44no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23C4×D4×C7314yes—
1102C23C23×C4×C7311yescharacteristic
1103C23C22×D4×C7311yescharacteristic
1104C23C22×D4×C7311yescharacteristic
1105C23C2×#41×C7311yescharacteristic
1106C23C2×#41×C7311yescharacteristic
1107C23C2×#41×C7311yescharacteristic
1108C23C2×#41×C7311yescharacteristic
1109C23H(5,𝔽2)×C7311yescharacteristic
1110C23H(5,𝔽2)×C7311yescharacteristic
1111C23H(5,𝔽2)×C7311yescharacteristic
1112C23H(5,𝔽2)×C7311yescharacteristic
1113C23H(5,𝔽2)×C7311yescharacteristic
1114C23H(5,𝔽2)×C7311yescharacteristic
1115C23H(5,𝔽2)×C7311yescharacteristic
1116C23H(5,𝔽2)×C7311yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4C4×D4×C7314yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C7311yescharacteristic
1251C22C2×C4×D4×C7311yescharacteristic
1252C22C4×#41×C7311yescharacteristic
1253C22#518×C7311yescharacteristic
1254C22#518×C7311yescharacteristic
1255C22#518×C7311yescharacteristic
1256C22#518×C7311yescharacteristic
1257C22#534×C7311yescharacteristic
1258C22#535×C7311yescharacteristic
1259C22#535×C7311yescharacteristic
1260C22#535×C7311yescharacteristic
1261C22#538×C7311yescharacteristic
1262C22#538×C7311yescharacteristic
1263C22#538×C7311yescharacteristic
1264C22#538×C7311yescharacteristic
1265C22#540×C7311yescharacteristic
1266C22#540×C7311yescharacteristic
1267C22#540×C7311yescharacteristic
1268C22#540×C7311yescharacteristic
1269C22D42×C7311yescharacteristic
1270C22#546×C7311yescharacteristic
1271C22#546×C7311yescharacteristic
1272C22#546×C7311yescharacteristic
1273C22#546×C7311yescharacteristic
1274C22#546×C7311yescharacteristic
1275C22#550×C7311yescharacteristic
1276C22#551×C7311yescharacteristic
1277C22#553×C7311yescharacteristic
1278C22#553×C7311yescharacteristic
1279C22#553×C7311yescharacteristic
1280C22#555×C7311yescharacteristic
1281C22#560×C7311yescharacteristic
1282C22#560×C7311yescharacteristic
1283C22#560×C7311yescharacteristic
1284C22H(3,𝔽4)×C7311yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C73×#232111yescharacteristic
1301C2C73×#232811yescharacteristic
1302C2C73×#233311yescharacteristic
1303C2C73×#235811yescharacteristic
1304C2C73×#236311yescharacteristic
1305C2C73×#236411yescharacteristic
1306C2C73×#237511yescharacteristic
1307C2C73×#267011yescharacteristic
1308C2C73×#267311yescharacteristic
1309C2C73×#269911yescharacteristic
1310C2C73×#270311yescharacteristic
1311C2C73×#270311yescharacteristic
1312C2C73×#271411yescharacteristic
1313C2C73×#275311yescharacteristic
1314C2C73×#275611yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC24C24×C73
prime radicalC2×#392×C73C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#390×C73C2semidirect
3. C2×#388×C73C2semidirect
4. C2×#386×C73C2semidirect
5. C2×#386×C73C2semidirect
6. C73×#1442C2semidirect
7. C73×#1440C2semidirect
8. C73×#1438C2semidirect
9. C73×#1438C2semidirect
10. C73×#1438C2semidirect
11. C73×#1437C2semidirect
12. C73×#1437C2semidirect
13. C73×#1437C2semidirect
14. C73×#1434C2semidirect
15. C73×C22⋊#95C2semidirect
37. #392×C73C4semidirect
79. C22×D4×C73C2×C4semidirect
141. C2×C22⋊C4×C73C2×C4semidirect
142. C2×C22⋊C4×C73C2×C4semidirect
143. C2×C22⋊C4×C73D4semidirect
162. #95×C73C2×C4semidirect
163. #95×C73D4semidirect
639. #14520C73direct (N × H)
659. C2×#390C2×C73semidirect
660. C2×#388C2×C73semidirect
661. C2×#386C2×C73semidirect
662. C2×#386C2×C73semidirect
663. #1442C2×C73semidirect
664. #1440C2×C73semidirect
665. #1438C2×C73semidirect
666. #1438C2×C73semidirect
667. #1438C2×C73semidirect
668. #1437C2×C73semidirect
669. #1437C2×C73semidirect
670. #1437C2×C73semidirect
671. #1434C2×C73semidirect
672. C22⋊#95C2×C73semidirect
673. C73#14520direct (N × H)
695. #392C4×C73semidirect
737. C22×D4C2×C4×C73semidirect
799. C2×C22⋊C4C2×C4×C73semidirect
800. C2×C22⋊C4C2×C4×C73semidirect
801. C2×C22⋊C4D4×C73semidirect
820. #95C2×C4×C73semidirect
821. #95D4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#392×C732
C2×#390×C732
C2×#388×C732
C2×#386×C732
C73×#14422
C73×#14402
C73×#14382
C73×#14372
C73×#14342
C73×C22⋊#952
#1452073