Finite Group Databasebeta

← C73×#14405 #32923809

Subgroups — C73×#14405 #32923809

Order 18688.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C73C211yesmaximal, characteristic, complemented
2C2×#388×C73C211yesmaximal, characteristic
3C2×#388×C73C211yesmaximal, characteristic
4C2×#385×C73C211yesmaximal, characteristic
5C2×#385×C73C211yesmaximal, characteristic
6C2×#385×C73C211yesmaximal, characteristic
7C2×#384×C73C211yesmaximal, characteristic, complemented
8C73×#1444C211yesmaximal, characteristic, complemented
9C73×#1444C211yesmaximal, characteristic, complemented
10C73×#1442C211yesmaximal, characteristic, complemented
11C73×#1441C211yesmaximal, characteristic, complemented
12C73×#1439C211yesmaximal, characteristic
13C73×#1439C211yesmaximal, characteristic
14C73×#1436C211yesmaximal, characteristic, complemented
15C73×#1434C211yesmaximal, characteristic, complemented
16C24×C4×C73C2211yescharacteristic
17C22×C4⋊C4×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C22×C4⋊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×C42×C73C2211yescharacteristic
34C22×C42×C73C2211yescharacteristic
35#389×C73—24no—
36#388×C73—24no—
37#388×C73C418yescomplemented
38#385×C73—24no—
39#385×C73—24no—
40#385×C73—24no—
41#384×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
56C2×#95×C73C2211yescharacteristic
57C2×#95×C73C2211yescharacteristic
58C25×C73C2311yescharacteristic
59C23×C4×C73—22no—
60C23×C4×C73—22no—
61C23×C4×C73—22no—
62C23×C4×C73—41no—
63C23×C4×C73—41no—
64C23×C4×C73—41no—
65C23×C4×C73—41no—
66C23×C4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C23×C4×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—22no—
94C2×C4⋊C4×C73—22no—
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—41no—
97C2×C4⋊C4×C73—41no—
98C2×C4⋊C4×C73—41no—
99C2×C4⋊C4×C73—41no—
100C2×C4⋊C4×C73—41no—
101C2×C4⋊C4×C73—41no—
102C2×C4⋊C4×C73—41no—
103C2×C4⋊C4×C73—41no—
104C2×C4⋊C4×C73—41no—
105C2×C4⋊C4×C73—41no—
106C2×C4⋊C4×C73—41no—
107C2×C4⋊C4×C73—41no—
108C2×C4⋊C4×C73C2×C414yescomplemented
109C2×C4⋊C4×C73D414yes—
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—41no—
120C2×C22⋊C4×C73—41no—
121C2×C22⋊C4×C73—41no—
122C2×C22⋊C4×C73—41no—
123C2×C22⋊C4×C73C2×C414yes—
124C2×C22⋊C4×C73C2×C414yes—
125C2×C22⋊C4×C73C2×C414yes—
126C2×C22⋊C4×C73D414yes—
127C2×C22⋊C4×C73Q814yes—
128C2×C42×C73—22no—
129C2×C42×C73—22no—
130C2×C42×C73—22no—
131C2×C42×C73—22no—
132C2×C42×C73—41no—
133C2×C42×C73C2×C414yescomplemented
134#95×C73—22no—
135#95×C73—22no—
136#95×C73—22no—
137#95×C73—22no—
138#95×C73—22no—
139#95×C73—22no—
140#95×C73—22no—
141#95×C73—22no—
142#95×C73—22no—
143#95×C73—22no—
144#95×C73—41no—
145#95×C73—41no—
146#95×C73—41no—
147#95×C73C2×C414yescomplemented
148#95×C73C2×C414yescomplemented
149#95×C73D414yes—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—21no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—21no—
160C24×C73—21no—
161C24×C73—21no—
162C24×C73C22×C412yes—
163C24×C73C2×D412yes—
164C24×C73C2×Q812yes—
165C24×C73C2411yescharacteristic
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
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—44no—
247C22×C4×C73—44no—
248C22×C4×C73—44no—
249C22×C4×C73—44no—
250C22×C4×C73—44no—
251C22×C4×C73—44no—
252C22×C4×C73—44no—
253C22×C4×C73C22×C412yes—
254C22×C4×C73C22×C412yes—
255C22×C4×C73C22×C412yes—
256C22×C4×C73C22×C412yes—
257C22×C4×C73C22×C412yes—
258C22×C4×C73C22×C412yes—
259C22×C4×C73C2×D412yes—
260C22×C4×C73C2×D412yes—
261C22×C4×C73C2×D412yes—
262C22×C4×C73C2×D412yes—
263C22×C4×C73C2×D412yes—
264C22×C4×C73C2×D412yes—
265C22×C4×C73C2×D412yes—
266C22×C4×C73C2×D412yes—
267C22×C4×C73C2×Q812yes—
268C22×C4×C73C2×Q812yes—
269C22×C4×C73#4112yes—
270C22×C4×C73#4112yes—
271C4⋊C4×C73—28no—
272C4⋊C4×C73—44no—
273C4⋊C4×C73—44no—
274C4⋊C4×C73—44no—
275C4⋊C4×C73—44no—
276C4⋊C4×C73—44no—
277C4⋊C4×C73—44no—
278C4⋊C4×C73—44no—
279C4⋊C4×C73—44no—
280C4⋊C4×C73—44no—
281C22⋊C4×C73—28no—
282C22⋊C4×C73—28no—
283C22⋊C4×C73—44no—
284C22⋊C4×C73—44no—
285C22⋊C4×C73—44no—
286C22⋊C4×C73C4⋊C4116yescomplemented
287C42×C73—28no—
288C42×C73—44no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—22no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—22no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73—41no—
319C23×C73—41no—
320C23×C73—41no—
321C23×C73—41no—
322C23×C73—41no—
323C23×C73C2×C4⋊C414yes—
324C23×C73C23×C411yescharacteristic
325C23×C73C22×D411yescharacteristic
326C23×C73C22×D411yescharacteristic
327C23×C73C22×D411yescharacteristic
328C23×C73C22×Q811yescharacteristic
329C23×C73C2×#4111yescharacteristic
330C23×C73C2×#4111yescharacteristic
331C23×C73H(5,𝔽2)11yescharacteristic
332C23×C73H(5,𝔽2)11yescharacteristic
333C23×C73H(5,𝔽2)11yescharacteristic
334C23×C73H(5,𝔽2)11yescharacteristic
335C23×C732−1+411yescharacteristic
336C23×C732−1+411yescharacteristic
337C23×C732−1+411yescharacteristic
338C23×C732−1+411yescharacteristic
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—22no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—22no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—22no—
373C2×C4×C73—22no—
374C2×C4×C73—22no—
375C2×C4×C73—22no—
376C2×C4×C73—22no—
377C2×C4×C73—22no—
378C2×C4×C73—22no—
379C2×C4×C73—22no—
380C2×C4×C73—22no—
381C2×C4×C73—416no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73—41no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—41no—
406C2×C4×C73—41no—
407C2×C4×C73—41no—
408C2×C4×C73—41no—
409C2×C4×C73—41no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—41no—
414C2×C4×C73—41no—
415C2×C4×C73—41no—
416C2×C4×C73—41no—
417C2×C4×C73—41no—
418C2×C4×C73—41no—
419C2×C4×C73—41no—
420C2×C4×C73—41no—
421C2×C4×C73—41no—
422C2×C4×C73—41no—
423C2×C4×C73—41no—
424C2×C4×C73—41no—
425C2×C4×C73—41no—
426C2×C4×C73—41no—
427C2×C4×C73—41no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73—41no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73C2×C4⋊C414yes—
435C2×C4×C73C2×C4⋊C414yes—
436C2×C4×C73C4×D414yes—
437C2×C4×C73C4×D414yes—
438C22×C73—24no—
439C22×C73—24no—
440C22×C73—24no—
441C22×C73—42no—
442C22×C73—42no—
443C22×C73—42no—
444C22×C73—42no—
445C22×C73—42no—
446C22×C73—42no—
447C22×C73—42no—
448C22×C73—42no—
449C22×C73—42no—
450C22×C73—42no—
451C22×C73—42no—
452C22×C73—42no—
453C22×C73C22×C4⋊C411yescharacteristic
454C22×C73C2×C4×D411yescharacteristic
455C22×C73C2×C4×D411yescharacteristic
456C22×C73#52011yescharacteristic
457C22×C73#52011yescharacteristic
458C22×C73#52011yescharacteristic
459C22×C73#52011yescharacteristic
460C22×C73#53411yescharacteristic
461C22×C73#53511yescharacteristic
462C22×C73#53511yescharacteristic
463C22×C73#53611yescharacteristic
464C22×C73#53611yescharacteristic
465C22×C73#53611yescharacteristic
466C22×C73#53911yescharacteristic
467C22×C73#53911yescharacteristic
468C22×C73#54211yescharacteristic
469C22×C73#54211yescharacteristic
470C22×C73#54411yescharacteristic
471C22×C73#54411yescharacteristic
472C22×C73D4211yescharacteristic
473C22×C73D4211yescharacteristic
474C22×C73D4211yescharacteristic
475C22×C73#54711yescharacteristic
476C22×C73#54711yescharacteristic
477C22×C73#54711yescharacteristic
478C22×C73#54811yescharacteristic
479C22×C73D4×Q811yescharacteristic
480C22×C73D4×Q811yescharacteristic
481C22×C73#55311yescharacteristic
482C22×C73#55411yescharacteristic
483C22×C73#55411yescharacteristic
484C22×C73#56011yescharacteristic
485C22×C73#56311yescharacteristic
486C22×C73#56311yescharacteristic
487C22×C73#56311yescharacteristic
488C4×C73—24no—
489C4×C73—24no—
490C4×C73—24no—
491C4×C73—24no—
492C4×C73—42no—
493C4×C73—42no—
494C4×C73—42no—
495C4×C73—42no—
496C4×C73—42no—
497C4×C73—42no—
498C4×C73—81no—
499C4×C73—81no—
500C4×C73—81no—
501C4×C73—81no—
502#14405C7311yesmaximal, characteristic, direct product factor, Sylow
503C2×C73—44no—
504C2×C73#231711yescharacteristic
505C2×C73#232211yescharacteristic
506C2×C73#232611yescharacteristic
507C2×C73D4×C4⋊C411yescharacteristic
508C2×C73D4×C4⋊C411yescharacteristic
509C2×C73#236111yescharacteristic
510C2×C73#238311yescharacteristic
511C2×C73#266911yescharacteristic
512C2×C73#267411yescharacteristic
513C2×C73#267711yescharacteristic
514C2×C73#268011yescharacteristic
515C2×C73#271811yescharacteristic
516C2×C73#272011yescharacteristic
517C2×C73#272911yescharacteristic
518C2×C73#279011yescharacteristic
519C2×#389C2×C7311yescharacteristic, complemented
520C2×#388C2×C7311yescharacteristic
521C2×#388C2×C7311yescharacteristic
522C2×#385C2×C7311yescharacteristic
523C2×#385C2×C7311yescharacteristic
524C2×#385C2×C7311yescharacteristic
525C2×#384C2×C7311yescharacteristic, complemented
526#1444C2×C7311yescharacteristic, complemented
527#1444C2×C7311yescharacteristic, complemented
528#1442C2×C7311yescharacteristic, complemented
529#1441C2×C7311yescharacteristic, complemented
530#1439C2×C7311yescharacteristic
531#1439C2×C7311yescharacteristic
532#1436C2×C7311yescharacteristic, complemented
533#1434C2×C7311yescharacteristic, complemented
534C73#1440511yescharacteristic, direct product factor, Sylow
535C24×C4C22×C7311yescharacteristic
536C22×C4⋊C4C22×C7311yescharacteristic
537C22×C4⋊C4C22×C7311yescharacteristic
538C22×C4⋊C4C22×C7311yescharacteristic
539C22×C4⋊C4C22×C7311yescharacteristic
540C22×C4⋊C4C22×C7311yescharacteristic
541C22×C4⋊C4C22×C7311yescharacteristic
542C22×C4⋊C4C22×C7311yescharacteristic
543C22×C4⋊C4C22×C7311yescharacteristic
544C22×C4⋊C4C22×C7311yescharacteristic
545C22×C4⋊C4C22×C7311yescharacteristic
546C22×C22⋊C4C22×C7311yescharacteristic
547C22×C22⋊C4C22×C7311yescharacteristic
548C22×C22⋊C4C22×C7311yescharacteristic
549C22×C22⋊C4C22×C7311yescharacteristic
550C22×C22⋊C4C22×C7311yescharacteristic
551C22×C22⋊C4C22×C7311yescharacteristic
552C22×C42C22×C7311yescharacteristic
553C22×C42C22×C7311yescharacteristic
554#389—24no—
555#388—24no—
556#388C4×C7318yescomplemented
557#385—24no—
558#385—24no—
559#385—24no—
560#384—24no—
561C2×#95C22×C7311yescharacteristic
562C2×#95C22×C7311yescharacteristic
563C2×#95C22×C7311yescharacteristic
564C2×#95C22×C7311yescharacteristic
565C2×#95C22×C7311yescharacteristic
566C2×#95C22×C7311yescharacteristic
567C2×#95C22×C7311yescharacteristic
568C2×#95C22×C7311yescharacteristic
569C2×#95C22×C7311yescharacteristic
570C2×#95C22×C7311yescharacteristic
571C2×#95C22×C7311yescharacteristic
572C2×#95C22×C7311yescharacteristic
573C2×#95C22×C7311yescharacteristic
574C2×#95C22×C7311yescharacteristic
575C2×#95C22×C7311yescharacteristic
576C2×#95C22×C7311yescharacteristic
577C25C23×C7311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4C23×C7311yescharacteristic
586C23×C4C23×C7311yescharacteristic
587C23×C4C23×C7311yescharacteristic
588C23×C4C23×C7311yescharacteristic
589C23×C4C23×C7311yescharacteristic
590C23×C4C23×C7311yescharacteristic
591C23×C4C23×C7311yescharacteristic
592C23×C4C23×C7311yescharacteristic
593C23×C4C23×C7311yescharacteristic
594C23×C4C23×C7311yescharacteristic
595C23×C4C23×C7311yescharacteristic
596C23×C4C23×C7311yescharacteristic
597C23×C4C23×C7311yescharacteristic
598C23×C4C23×C7311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4C2×C4×C7314yescomplemented
628C2×C4⋊C4D4×C7314yes—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4C2×C4×C7314yes—
643C2×C22⋊C4C2×C4×C7314yes—
644C2×C22⋊C4C2×C4×C7314yes—
645C2×C22⋊C4D4×C7314yes—
646C2×C22⋊C4Q8×C7314yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—41no—
652C2×C42C2×C4×C7314yescomplemented
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95C2×C4×C7314yescomplemented
667#95C2×C4×C7314yescomplemented
668#95D4×C7314yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C7312yes—
682C24C2×D4×C7312yes—
683C24C2×Q8×C7312yes—
684C24C24×C7311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C7312yes—
773C22×C4C22×C4×C7312yes—
774C22×C4C22×C4×C7312yes—
775C22×C4C22×C4×C7312yes—
776C22×C4C22×C4×C7312yes—
777C22×C4C22×C4×C7312yes—
778C22×C4C2×D4×C7312yes—
779C22×C4C2×D4×C7312yes—
780C22×C4C2×D4×C7312yes—
781C22×C4C2×D4×C7312yes—
782C22×C4C2×D4×C7312yes—
783C22×C4C2×D4×C7312yes—
784C22×C4C2×D4×C7312yes—
785C22×C4C2×D4×C7312yes—
786C22×C4C2×Q8×C7312yes—
787C22×C4C2×Q8×C7312yes—
788C22×C4#41×C7312yes—
789C22×C4#41×C7312yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C73116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C7314yes—
843C23C23×C4×C7311yescharacteristic
844C23C22×D4×C7311yescharacteristic
845C23C22×D4×C7311yescharacteristic
846C23C22×D4×C7311yescharacteristic
847C23C22×Q8×C7311yescharacteristic
848C23C2×#41×C7311yescharacteristic
849C23C2×#41×C7311yescharacteristic
850C23H(5,𝔽2)×C7311yescharacteristic
851C23H(5,𝔽2)×C7311yescharacteristic
852C23H(5,𝔽2)×C7311yescharacteristic
853C23H(5,𝔽2)×C7311yescharacteristic
854C232−1+4×C7311yescharacteristic
855C232−1+4×C7311yescharacteristic
856C232−1+4×C7311yescharacteristic
857C232−1+4×C7311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4C2×C4⋊C4×C7314yes—
954C2×C4C2×C4⋊C4×C7314yes—
955C2×C4C4×D4×C7314yes—
956C2×C4C4×D4×C7314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C7311yescharacteristic
973C22C2×C4×D4×C7311yescharacteristic
974C22C2×C4×D4×C7311yescharacteristic
975C22#520×C7311yescharacteristic
976C22#520×C7311yescharacteristic
977C22#520×C7311yescharacteristic
978C22#520×C7311yescharacteristic
979C22#534×C7311yescharacteristic
980C22#535×C7311yescharacteristic
981C22#535×C7311yescharacteristic
982C22#536×C7311yescharacteristic
983C22#536×C7311yescharacteristic
984C22#536×C7311yescharacteristic
985C22#539×C7311yescharacteristic
986C22#539×C7311yescharacteristic
987C22#542×C7311yescharacteristic
988C22#542×C7311yescharacteristic
989C22#544×C7311yescharacteristic
990C22#544×C7311yescharacteristic
991C22D42×C7311yescharacteristic
992C22D42×C7311yescharacteristic
993C22D42×C7311yescharacteristic
994C22#547×C7311yescharacteristic
995C22#547×C7311yescharacteristic
996C22#547×C7311yescharacteristic
997C22#548×C7311yescharacteristic
998C22D4×Q8×C7311yescharacteristic
999C22D4×Q8×C7311yescharacteristic
1000C22#553×C7311yescharacteristic
1001C22#554×C7311yescharacteristic
1002C22#554×C7311yescharacteristic
1003C22#560×C7311yescharacteristic
1004C22#563×C7311yescharacteristic
1005C22#563×C7311yescharacteristic
1006C22#563×C7311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C73×#231711yescharacteristic
1023C2C73×#232211yescharacteristic
1024C2C73×#232611yescharacteristic
1025C2D4×C4⋊C4×C7311yescharacteristic
1026C2D4×C4⋊C4×C7311yescharacteristic
1027C2C73×#236111yescharacteristic
1028C2C73×#238311yescharacteristic
1029C2C73×#266911yescharacteristic
1030C2C73×#267411yescharacteristic
1031C2C73×#267711yescharacteristic
1032C2C73×#268011yescharacteristic
1033C2C73×#271811yescharacteristic
1034C2C73×#272011yescharacteristic
1035C2C73×#272911yescharacteristic
1036C2C73×#279011yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC24C24×C73
prime radicalC25×C73C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C73C2semidirect
7. C2×#384×C73C2semidirect
8. C73×#1444C2semidirect
9. C73×#1444C2semidirect
10. C73×#1442C2semidirect
11. C73×#1441C2semidirect
14. C73×#1436C2semidirect
15. C73×#1434C2semidirect
37. #388×C73C4semidirect
108. C2×C4⋊C4×C73C2×C4semidirect
133. C2×C42×C73C2×C4semidirect
147. #95×C73C2×C4semidirect
148. #95×C73C2×C4semidirect
286. C22⋊C4×C73C4⋊C4semidirect
502. #14405C73direct (N × H)
519. C2×#389C2×C73semidirect
525. C2×#384C2×C73semidirect
526. #1444C2×C73semidirect
527. #1444C2×C73semidirect
528. #1442C2×C73semidirect
529. #1441C2×C73semidirect
532. #1436C2×C73semidirect
533. #1434C2×C73semidirect
534. C73#14405direct (N × H)
556. #388C4×C73semidirect
627. C2×C4⋊C4C2×C4×C73semidirect
652. C2×C42C2×C4×C73semidirect
666. #95C2×C4×C73semidirect
667. #95C2×C4×C73semidirect
805. C22⋊C4C4⋊C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C732
C2×#388×C732
C2×#385×C732
C2×#384×C732
C73×#14442
C73×#14422
C73×#14412
C73×#14392
C73×#14362
C73×#14342
#1440573