Finite Group Databasebeta

← C73×#14116 #32923520

Subgroups — C73×#14116 #32923520

Order 18688.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1022 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×C4×C22⋊C4×C73C211yesmaximal, characteristic
6C73×#1442C211yesmaximal, characteristic, complemented
7C73×#1441C211yesmaximal, characteristic, complemented
8C73×#1439C211yesmaximal, characteristic
9C73×#1439C211yesmaximal, characteristic
10C73×#1436C211yesmaximal, characteristic, complemented
11C73×#1436C211yesmaximal, characteristic, complemented
12C73×#1436C211yesmaximal, characteristic, complemented
13C73×C4⋊#95C211yesmaximal, characteristic, complemented
14C73×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C73C211yesmaximal, 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×C22⋊C4×C73C2211yescharacteristic
24C22×C22⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C42×C73C2211yescharacteristic
30C22×C42×C73C2211yescharacteristic
31C22×C42×C73C2211yescharacteristic
32C22×C42×C73C2211yescharacteristic
33#389×C73—24no—
34#388×C73—24no—
35#388×C73C418yescomplemented
36#385×C73—24no—
37C4×C22⋊C4×C73—24no—
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C2×#95×C73C2211yescharacteristic
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
57C23×C4×C73—22no—
58C23×C4×C73—22no—
59C23×C4×C73—22no—
60C23×C4×C73—22no—
61C23×C4×C73—22no—
62C23×C4×C73—41no—
63C23×C4×C73—41no—
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
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
78C2×C4⋊C4×C73—22no—
79C2×C4⋊C4×C73—22no—
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—41no—
92C2×C4⋊C4×C73—41no—
93C2×C4⋊C4×C73—41no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73C2×C414yescomplemented
96C2×C22⋊C4×C73—22no—
97C2×C22⋊C4×C73—22no—
98C2×C22⋊C4×C73—22no—
99C2×C22⋊C4×C73—22no—
100C2×C22⋊C4×C73—22no—
101C2×C22⋊C4×C73—22no—
102C2×C22⋊C4×C73—22no—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73—22no—
105C2×C22⋊C4×C73—41no—
106C2×C22⋊C4×C73—41no—
107C2×C22⋊C4×C73—41no—
108C2×C22⋊C4×C73—41no—
109C2×C22⋊C4×C73C2×C414yes—
110C2×C22⋊C4×C73C2×C414yes—
111C2×C22⋊C4×C73C2×C414yes—
112C2×C22⋊C4×C73D414yes—
113C2×C22⋊C4×C73Q814yes—
114C2×C42×C73—22no—
115C2×C42×C73—22no—
116C2×C42×C73—22no—
117C2×C42×C73—22no—
118C2×C42×C73—22no—
119C2×C42×C73—22no—
120C2×C42×C73—41no—
121C2×C42×C73—41no—
122C2×C42×C73—41no—
123C2×C42×C73—41no—
124C2×C42×C73—41no—
125C2×C42×C73C2×C414yescomplemented
126#95×C73—22no—
127#95×C73—22no—
128#95×C73—22no—
129#95×C73—22no—
130#95×C73—22no—
131#95×C73—22no—
132#95×C73—22no—
133#95×C73—22no—
134#95×C73—22no—
135#95×C73—22no—
136#95×C73—22no—
137#95×C73—22no—
138#95×C73—41no—
139#95×C73—41no—
140#95×C73—41no—
141#95×C73C2×C414yescomplemented
142#95×C73C2×C414yescomplemented
143#95×C73D414yes—
144C24×C73—21no—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73—21no—
148C24×C73—21no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73C22×C412yes—
157C24×C73C2×D412yes—
158C24×C73C2×Q812yes—
159C24×C73C2411yescharacteristic
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
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—28no—
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—44no—
240C22×C4×C73—44no—
241C22×C4×C73—44no—
242C22×C4×C73—44no—
243C22×C4×C73—44no—
244C22×C4×C73—44no—
245C22×C4×C73C22×C412yes—
246C22×C4×C73C22×C412yes—
247C22×C4×C73C22×C412yes—
248C22×C4×C73C22×C412yes—
249C22×C4×C73C22×C412yes—
250C22×C4×C73C22×C412yes—
251C22×C4×C73C2×D412yes—
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2×D412yes—
254C22×C4×C73C2×D412yes—
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2×Q812yes—
257C22×C4×C73C2×Q812yes—
258C22×C4×C73#4112yes—
259C22×C4×C73#4112yes—
260C22×C4×C73#4112yes—
261C22×C4×C73#4112yes—
262C22×C4×C73#4112yes—
263C22×C4×C73#4112yes—
264C22×C4×C73#4112yes—
265C4⋊C4×C73—28no—
266C4⋊C4×C73—44no—
267C4⋊C4×C73—44no—
268C4⋊C4×C73—44no—
269C4⋊C4×C73—44no—
270C4⋊C4×C73—44no—
271C22⋊C4×C73—28no—
272C22⋊C4×C73—28no—
273C22⋊C4×C73—44no—
274C22⋊C4×C73—44no—
275C22⋊C4×C73—44no—
276C22⋊C4×C73C4⋊C4116yescomplemented
277C42×C73—44no—
278C42×C73—44no—
279C42×C73—44no—
280C42×C73—44no—
281C23×C73—22no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
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—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
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×C73C2×C4⋊C414yes—
316C23×C73C23×C411yescharacteristic
317C23×C73C22×D411yescharacteristic
318C23×C73C22×D411yescharacteristic
319C23×C73C22×Q811yescharacteristic
320C23×C73C2×#4111yescharacteristic
321C23×C73C2×#4111yescharacteristic
322C23×C73C2×#4111yescharacteristic
323C23×C73C2×#4111yescharacteristic
324C23×C73C2×#4111yescharacteristic
325C23×C73C2×#4111yescharacteristic
326C23×C73C2×#4111yescharacteristic
327C23×C73H(5,𝔽2)11yescharacteristic
328C23×C73H(5,𝔽2)11yescharacteristic
329C23×C73H(5,𝔽2)11yescharacteristic
330C23×C732−1+411yescharacteristic
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
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—416no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
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×C73C2×C4⋊C414yes—
427C2×C4×C73C2×C4⋊C414yes—
428C2×C4×C73C4×D414yes—
429C2×C4×C73#12414yes—
430C22×C73—24no—
431C22×C73—24no—
432C22×C73—24no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73—42no—
438C22×C73—42no—
439C22×C73—42no—
440C22×C73—42no—
441C22×C73—42no—
442C22×C73—42no—
443C22×C73—42no—
444C22×C73—42no—
445C22×C73C22×C4⋊C411yescharacteristic
446C22×C73C2×C4×D411yescharacteristic
447C22×C73C4×#4111yescharacteristic
448C22×C73C4×#4111yescharacteristic
449C22×C73C4×#4111yescharacteristic
450C22×C73#51811yescharacteristic
451C22×C73#52011yescharacteristic
452C22×C73#52511yescharacteristic
453C22×C73#52511yescharacteristic
454C22×C73C2×#12411yescharacteristic
455C22×C73#52911yescharacteristic
456C22×C73#52911yescharacteristic
457C22×C73#53211yescharacteristic
458C22×C73#53311yescharacteristic
459C22×C73#53311yescharacteristic
460C22×C73#53811yescharacteristic
461C22×C73#53911yescharacteristic
462C22×C73#54011yescharacteristic
463C22×C73#54211yescharacteristic
464C22×C73D4211yescharacteristic
465C22×C73#54611yescharacteristic
466C22×C73#54611yescharacteristic
467C22×C73#54611yescharacteristic
468C22×C73#54611yescharacteristic
469C22×C73#54711yescharacteristic
470C22×C73D4×Q811yescharacteristic
471C22×C73#55111yescharacteristic
472C22×C73#55211yescharacteristic
473C22×C73#55311yescharacteristic
474C22×C73#55311yescharacteristic
475C22×C73#55311yescharacteristic
476C22×C73#55411yescharacteristic
477C22×C73#55411yescharacteristic
478C22×C73#55411yescharacteristic
479C22×C73#55611yescharacteristic
480C4×C73—24no—
481C4×C73—24no—
482C4×C73—24no—
483C4×C73—24no—
484C4×C73—42no—
485C4×C73—42no—
486C4×C73—42no—
487C4×C73—42no—
488C4×C73—42no—
489C4×C73—42no—
490C4×C73—42no—
491C4×C73—42no—
492C4×C73—81no—
493C4×C73—81no—
494#14116C7311yesmaximal, characteristic, direct product factor, Sylow
495C2×C73—44no—
496C2×C73#229611yescharacteristic
497C2×C73C4×#12411yescharacteristic
498C2×C73#233511yescharacteristic
499C2×C73D4×C4⋊C411yescharacteristic
500C2×C73#234911yescharacteristic
501C2×C73#236411yescharacteristic
502C2×C73#237311yescharacteristic
503C2×C73#246411yescharacteristic
504C2×C73#246611yescharacteristic
505C2×C73#247011yescharacteristic
506C2×C73#247211yescharacteristic
507C2×C73#249211yescharacteristic
508C2×C73#252211yescharacteristic
509C2×C73#255611yescharacteristic
510C2×C73#258711yescharacteristic
511C2×#389C2×C7311yescharacteristic, complemented
512C2×#388C2×C7311yescharacteristic
513C2×#388C2×C7311yescharacteristic
514C2×#385C2×C7311yescharacteristic
515C2×C4×C22⋊C4C2×C7311yescharacteristic
516#1442C2×C7311yescharacteristic, complemented
517#1441C2×C7311yescharacteristic, complemented
518#1439C2×C7311yescharacteristic
519#1439C2×C7311yescharacteristic
520#1436C2×C7311yescharacteristic, complemented
521#1436C2×C7311yescharacteristic, complemented
522#1436C2×C7311yescharacteristic, complemented
523C4⋊#95C2×C7311yescharacteristic, complemented
524C22⋊#95C2×C7311yescharacteristic
525C4×#95C2×C7311yescharacteristic, complemented
526C73#1411611yescharacteristic, direct product factor, Sylow
527C24×C4C22×C7311yescharacteristic
528C22×C4⋊C4C22×C7311yescharacteristic
529C22×C4⋊C4C22×C7311yescharacteristic
530C22×C4⋊C4C22×C7311yescharacteristic
531C22×C4⋊C4C22×C7311yescharacteristic
532C22×C4⋊C4C22×C7311yescharacteristic
533C22×C4⋊C4C22×C7311yescharacteristic
534C22×C22⋊C4C22×C7311yescharacteristic
535C22×C22⋊C4C22×C7311yescharacteristic
536C22×C22⋊C4C22×C7311yescharacteristic
537C22×C22⋊C4C22×C7311yescharacteristic
538C22×C22⋊C4C22×C7311yescharacteristic
539C22×C22⋊C4C22×C7311yescharacteristic
540C22×C42C22×C7311yescharacteristic
541C22×C42C22×C7311yescharacteristic
542C22×C42C22×C7311yescharacteristic
543C22×C42C22×C7311yescharacteristic
544#389—24no—
545#388—24no—
546#388C4×C7318yescomplemented
547#385—24no—
548C4×C22⋊C4—24no—
549C2×#95C22×C7311yescharacteristic
550C2×#95C22×C7311yescharacteristic
551C2×#95C22×C7311yescharacteristic
552C2×#95C22×C7311yescharacteristic
553C2×#95C22×C7311yescharacteristic
554C2×#95C22×C7311yescharacteristic
555C2×#95C22×C7311yescharacteristic
556C2×#95C22×C7311yescharacteristic
557C2×#95C22×C7311yescharacteristic
558C2×#95C22×C7311yescharacteristic
559C2×#95C22×C7311yescharacteristic
560C2×#95C22×C7311yescharacteristic
561C2×#95C22×C7311yescharacteristic
562C2×#95C22×C7311yescharacteristic
563C2×#95C22×C7311yescharacteristic
564C2×#95C22×C7311yescharacteristic
565C2×#95C22×C7311yescharacteristic
566C2×#95C22×C7311yescharacteristic
567C25C23×C7311yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4C23×C7311yescharacteristic
576C23×C4C23×C7311yescharacteristic
577C23×C4C23×C7311yescharacteristic
578C23×C4C23×C7311yescharacteristic
579C23×C4C23×C7311yescharacteristic
580C23×C4C23×C7311yescharacteristic
581C23×C4C23×C7311yescharacteristic
582C23×C4C23×C7311yescharacteristic
583C23×C4C23×C7311yescharacteristic
584C23×C4C23×C7311yescharacteristic
585C23×C4C23×C7311yescharacteristic
586C23×C4C23×C7311yescharacteristic
587C23×C4C23×C7311yescharacteristic
588C23×C4C23×C7311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C2×C4×C7314yescomplemented
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—41no—
620C2×C22⋊C4C2×C4×C7314yes—
621C2×C22⋊C4C2×C4×C7314yes—
622C2×C22⋊C4C2×C4×C7314yes—
623C2×C22⋊C4D4×C7314yes—
624C2×C22⋊C4Q8×C7314yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42—22no—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—41no—
636C2×C42C2×C4×C7314yescomplemented
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95C2×C4×C7314yescomplemented
653#95C2×C4×C7314yescomplemented
654#95D4×C7314yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C7312yes—
668C24C2×D4×C7312yes—
669C24C2×Q8×C7312yes—
670C24C24×C7311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—28no—
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—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4C22×C4×C7312yes—
757C22×C4C22×C4×C7312yes—
758C22×C4C22×C4×C7312yes—
759C22×C4C22×C4×C7312yes—
760C22×C4C22×C4×C7312yes—
761C22×C4C22×C4×C7312yes—
762C22×C4C2×D4×C7312yes—
763C22×C4C2×D4×C7312yes—
764C22×C4C2×D4×C7312yes—
765C22×C4C2×D4×C7312yes—
766C22×C4C2×D4×C7312yes—
767C22×C4C2×Q8×C7312yes—
768C22×C4C2×Q8×C7312yes—
769C22×C4#41×C7312yes—
770C22×C4#41×C7312yes—
771C22×C4#41×C7312yes—
772C22×C4#41×C7312yes—
773C22×C4#41×C7312yes—
774C22×C4#41×C7312yes—
775C22×C4#41×C7312yes—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4C4⋊C4×C73116yescomplemented
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊C4×C7314yes—
827C23C23×C4×C7311yescharacteristic
828C23C22×D4×C7311yescharacteristic
829C23C22×D4×C7311yescharacteristic
830C23C22×Q8×C7311yescharacteristic
831C23C2×#41×C7311yescharacteristic
832C23C2×#41×C7311yescharacteristic
833C23C2×#41×C7311yescharacteristic
834C23C2×#41×C7311yescharacteristic
835C23C2×#41×C7311yescharacteristic
836C23C2×#41×C7311yescharacteristic
837C23C2×#41×C7311yescharacteristic
838C23H(5,𝔽2)×C7311yescharacteristic
839C23H(5,𝔽2)×C7311yescharacteristic
840C23H(5,𝔽2)×C7311yescharacteristic
841C232−1+4×C7311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
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—416no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
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×C4C2×C4⋊C4×C7314yes—
938C2×C4C2×C4⋊C4×C7314yes—
939C2×C4C4×D4×C7314yes—
940C2×C4#124×C7314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊C4×C7311yescharacteristic
957C22C2×C4×D4×C7311yescharacteristic
958C22C4×#41×C7311yescharacteristic
959C22C4×#41×C7311yescharacteristic
960C22C4×#41×C7311yescharacteristic
961C22#518×C7311yescharacteristic
962C22#520×C7311yescharacteristic
963C22#525×C7311yescharacteristic
964C22#525×C7311yescharacteristic
965C22C2×#124×C7311yescharacteristic
966C22#529×C7311yescharacteristic
967C22#529×C7311yescharacteristic
968C22#532×C7311yescharacteristic
969C22#533×C7311yescharacteristic
970C22#533×C7311yescharacteristic
971C22#538×C7311yescharacteristic
972C22#539×C7311yescharacteristic
973C22#540×C7311yescharacteristic
974C22#542×C7311yescharacteristic
975C22D42×C7311yescharacteristic
976C22#546×C7311yescharacteristic
977C22#546×C7311yescharacteristic
978C22#546×C7311yescharacteristic
979C22#546×C7311yescharacteristic
980C22#547×C7311yescharacteristic
981C22D4×Q8×C7311yescharacteristic
982C22#551×C7311yescharacteristic
983C22#552×C7311yescharacteristic
984C22#553×C7311yescharacteristic
985C22#553×C7311yescharacteristic
986C22#553×C7311yescharacteristic
987C22#554×C7311yescharacteristic
988C22#554×C7311yescharacteristic
989C22#554×C7311yescharacteristic
990C22#556×C7311yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C73×#229611yescharacteristic
1007C2C4×#124×C7311yescharacteristic
1008C2C73×#233511yescharacteristic
1009C2D4×C4⋊C4×C7311yescharacteristic
1010C2C73×#234911yescharacteristic
1011C2C73×#236411yescharacteristic
1012C2C73×#237311yescharacteristic
1013C2C73×#246411yescharacteristic
1014C2C73×#246611yescharacteristic
1015C2C73×#247011yescharacteristic
1016C2C73×#247211yescharacteristic
1017C2C73×#249211yescharacteristic
1018C2C73×#252211yescharacteristic
1019C2C73×#255611yescharacteristic
1020C2C73×#258711yescharacteristic
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
6. C73×#1442C2semidirect
7. C73×#1441C2semidirect
10. C73×#1436C2semidirect
11. C73×#1436C2semidirect
12. C73×#1436C2semidirect
13. C73×C4⋊#95C2semidirect
15. C4×#95×C73C2semidirect
35. #388×C73C4semidirect
95. C2×C4⋊C4×C73C2×C4semidirect
125. C2×C42×C73C2×C4semidirect
141. #95×C73C2×C4semidirect
142. #95×C73C2×C4semidirect
276. C22⋊C4×C73C4⋊C4semidirect
494. #14116C73direct (N × H)
511. C2×#389C2×C73semidirect
516. #1442C2×C73semidirect
517. #1441C2×C73semidirect
520. #1436C2×C73semidirect
521. #1436C2×C73semidirect
522. #1436C2×C73semidirect
523. C4⋊#95C2×C73semidirect
525. C4×#95C2×C73semidirect
526. C73#14116direct (N × H)
546. #388C4×C73semidirect
606. C2×C4⋊C4C2×C4×C73semidirect
636. C2×C42C2×C4×C73semidirect
652. #95C2×C4×C73semidirect
653. #95C2×C4×C73semidirect
787. 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×C4×C22⋊C4×C732
C73×#14422
C73×#14412
C73×#14392
C73×#14362
C73×C4⋊#952
C73×C22⋊#952
C4×#95×C732
#1411673