Finite Group Databasebeta

← #32991978

Subgroups — #32991978

Order 18688.

926 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556501C211yesmaximal, characteristic
2C2×#17988486C211yesmaximal, characteristic
3C2×#17988350C211yesmaximal, characteristic
4C2×#17988349C211yesmaximal, characteristic
5C2×#17988349C211yesmaximal, characteristic
6#22608160C211yesmaximal, characteristic
7C2×#340×C73C211yesmaximal, characteristic
8C23×#10596831C2211yescharacteristic
9C22×C4⋊Dic73—21no—
10C22×C4⋊Dic73C2211yescharacteristic
11C22×C4⋊Dic73C2211yescharacteristic
12C22×C4×Dic73C2211yescharacteristic
13C2×#14556501—22no—
14C2×#14556501—22no—
15C2×#14556501—22no—
16#17988486—22no—
17#17988486C414yescomplemented
18C2×#14556498—21no—
19C2×#14556498—21no—
20C2×#14556498—21no—
21#17988350—22no—
22#17988349—22no—
23#17988349C414yescomplemented
24C23×C8×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C22×C4⋊C4×C73C2211yescharacteristic
27#340×C73C414yescomplemented
28C23×Dic73—21no—
29C23×Dic73—21no—
30C23×Dic73D411yescharacteristic
31C23×Dic73D411yescharacteristic
32C22×#10596831—21no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35C22×#10596831—21no—
36C22×#10596831C2×C412yes—
37C22×#10596831D412yes—
38C22×#10596831Q812yes—
39C2×C4⋊Dic73—24no—
40C2×C4⋊Dic73—21no—
41C2×C4⋊Dic73—21no—
42C2×C4⋊Dic73—21no—
43C2×C4⋊Dic73—21no—
44C2×C4⋊Dic73—21no—
45C2×C4⋊Dic73—21no—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—21no—
49C2×C4⋊Dic73—21no—
50C2×C4⋊Dic73—42no—
51C2×C4⋊Dic73—42no—
52C2×C4⋊Dic73C2×C412yes—
53C2×C4⋊Dic73C2×C412yes—
54C2×C4×Dic73—21no—
55C2×C4×Dic73—21no—
56C2×C4×Dic73—21no—
57C2×C4×Dic73—21no—
58C2×C4×Dic73C2×C412yes—
59C2×C4×Dic73D412yes—
60#14556501—28no—
61#14556498—24no—
62#14556498—42no—
63#14556498—42no—
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C22×C8×C73—21no—
68C22×C8×C73—21no—
69C22×C8×C73—21no—
70C22×C8×C73—21no—
71C22×C8×C73C2×C412yes—
72C22×C8×C73D412yes—
73C22×C8×C73Q812yes—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C4⋊C4×C73—21no—
82C2×C4⋊C4×C73C2×C412yes—
83C2×C4⋊C4×C73C2×C412yes—
84C2×C4⋊C4×C73C2×C412yes—
85C2×C4⋊C4×C73C2×C412yes—
86C22×Dic73—21no—
87C22×Dic73—21no—
88C22×Dic73—21no—
89C22×Dic73—21no—
90C22×Dic73—21no—
91C22×Dic73—21no—
92C22×Dic73—21no—
93C22×Dic73—21no—
94C22×Dic73—21no—
95C22×Dic73—21no—
96C22×Dic73—21no—
97C22×Dic73—21no—
98C22×Dic73—22no—
99C22×Dic73—22no—
100C22×Dic73—41no—
101C22×Dic73—41no—
102C22×Dic73—41no—
103C22×Dic73—41no—
104C22×Dic73—41no—
105C22×Dic73—41no—
106C22×Dic73—41no—
107C22×Dic73—41no—
108C22×Dic73—41no—
109C22×Dic73—41no—
110C22×Dic73—41no—
111C22×Dic73—41no—
112C22×Dic73C22⋊C412yes—
113C22×Dic73C22⋊C412yes—
114C2×#10596831—22no—
115C2×#10596831—22no—
116C2×#10596831—22no—
117C2×#10596831—22no—
118C2×#10596831—22no—
119C2×#10596831—22no—
120C2×#10596831C4⋊C414yescomplemented
121C4⋊Dic73—22no—
122C4⋊Dic73—22no—
123C4⋊Dic73—22no—
124C4⋊Dic73—22no—
125C4⋊Dic73—48no—
126C4⋊Dic73—41no—
127C4⋊Dic73—41no—
128C4⋊Dic73—41no—
129C4⋊Dic73—41no—
130C4×Dic73—22no—
131C4×Dic73—22no—
132C4×Dic73—22no—
133C4×Dic73—22no—
134C24×C73C2×D411yescharacteristic
135C22×C4×C73—22no—
136C22×C4×C73—22no—
137C22×C4×C73—22no—
138C22×C4×C73—22no—
139C22×C4×C73—41no—
140C22×C4×C73—41no—
141C22×C4×C73—41no—
142C22×C4×C73—41no—
143C22×C4×C73—41no—
144C22×C4×C73—41no—
145C22×C4×C73—41no—
146C22×C4×C73—41no—
147C22×C4×C73—41no—
148C22×C4×C73—41no—
149C22×C4×C73C22×C411yescharacteristic
150C22×C4×C73C22×C411yescharacteristic
151C22×C4×C73C22×C411yescharacteristic
152C22×C4×C73C2×D411yescharacteristic
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155C22×C4×C73C2×Q811yescharacteristic
156C22×C4×C73C2×Q811yescharacteristic
157C22×C4×C73#4111yescharacteristic
158C22×C4×C73#4111yescharacteristic
159C22×C4×C73#4111yescharacteristic
160C22×C4×C73#4111yescharacteristic
161C22×C4×C73#4111yescharacteristic
162C22×C4×C73#4111yescharacteristic
163C2×C8×C73—22no—
164C2×C8×C73—22no—
165C2×C8×C73—22no—
166C2×C8×C73—22no—
167C2×C8×C73—22no—
168C2×C8×C73—22no—
169C2×C8×C73C4⋊C414yescomplemented
170C4⋊C4×C73—22no—
171C4⋊C4×C73—22no—
172C4⋊C4×C73—22no—
173C4⋊C4×C73—22no—
174C4⋊C4×C73—22no—
175C4⋊C4×C73—41no—
176C4⋊C4×C73—41no—
177C4⋊C4×C73C4214yes—
178C23×C73C2×C22⋊C411yescharacteristic
179C23×C73C4×D411yescharacteristic
180C23×C73C4×D411yescharacteristic
181C23×C73#12111yescharacteristic
182C23×C73#12111yescharacteristic
183C23×C73#12411yescharacteristic
184C23×C73C4⋊Q811yescharacteristic
185C23×C73AGL(1,ℤ/8)11yescharacteristic
186C23×C73AGL(1,ℤ/8)11yescharacteristic
187C23×C73AGL(1,ℤ/8)11yescharacteristic
188C23×C73AGL(1,ℤ/8)11yescharacteristic
189C23×C73#13711yescharacteristic
190C23×C73#13711yescharacteristic
191C23×C73#13711yescharacteristic
192C23×C73#13711yescharacteristic
193C2×C4×C73—24no—
194C2×C4×C73—42no—
195C2×C4×C73—42no—
196C2×C4×C73—42no—
197C2×C4×C73—42no—
198C2×C4×C73—42no—
199C2×C4×C73—42no—
200C2×C4×C73—42no—
201C2×C4×C73—42no—
202C2×C4×C73—42no—
203C2×C4×C73—81no—
204C2×C4×C73—81no—
205C2×C4×C73—81no—
206C2×C4×C73—81no—
207C2×C4×C73C2×C4211yescharacteristic
208C2×C4×C73C2×C4⋊C411yescharacteristic
209C2×C4×C73C2×C4⋊C411yescharacteristic
210C2×C4×C73#11711yescharacteristic
211C2×C4×C73#11711yescharacteristic
212C2×C4×C73#11711yescharacteristic
213C2×C4×C73C4×D411yescharacteristic
214C2×C4×C73C4×D411yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×Q811yescharacteristic
220C2×C4×C73C4×Q811yescharacteristic
221C2×C4×C73C4×Q811yescharacteristic
222C2×C4×C73C4×Q811yescharacteristic
223C2×C4×C73#12011yescharacteristic
224C2×C4×C73C22⋊Q811yescharacteristic
225C2×C4×C73C22⋊Q811yescharacteristic
226C2×C4×C73C22⋊Q811yescharacteristic
227C2×C4×C73C22⋊Q811yescharacteristic
228C2×C4×C73#12311yescharacteristic
229C2×C4×C73#12311yescharacteristic
230C2×C4×C73#12311yescharacteristic
231C2×C4×C73#12511yescharacteristic
232C2×C4×C73#12511yescharacteristic
233C2×C4×C73#12611yescharacteristic
234C2×C4×C73#12611yescharacteristic
235C2×Dic73—22no—
236C2×Dic73—22no—
237C2×Dic73—22no—
238C2×Dic73—22no—
239C2×Dic73—22no—
240C2×Dic73—22no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—42no—
250C2×Dic73—42no—
251C2×Dic73—42no—
252C2×Dic73—42no—
253C2×Dic73—42no—
254C2×Dic73—42no—
255C2×Dic73—81no—
256C2×Dic73—81no—
257C2×Dic73—81no—
258C2×Dic73—81no—
259C2×Dic73—81no—
260C2×Dic73—81no—
261C2×Dic73—81no—
262C2×Dic73—81no—
263C8×C73—24no—
264#10596831—24no—
265C22×C73C4×C22⋊C411yescharacteristic
266C22×C73#38611yescharacteristic
267C22×C73#38811yescharacteristic
268C22×C73#38811yescharacteristic
269C22×C73#38911yescharacteristic
270C22×C73#38911yescharacteristic
271C22×C73#39111yescharacteristic
272C22×C73#41711yescharacteristic
273C22×C73#41711yescharacteristic
274C22×C73#41811yescharacteristic
275C22×C73#41911yescharacteristic
276C22×C73#44011yescharacteristic
277C22×C73#44011yescharacteristic
278C22×C73#44011yescharacteristic
279C22×C73#44011yescharacteristic
280C22×C73#44111yescharacteristic
281C22×C73#44111yescharacteristic
282C22×C73#44211yescharacteristic
283C22×C73#44211yescharacteristic
284C22×C73#46811yescharacteristic
285C22×C73#46811yescharacteristic
286C22×C73#46811yescharacteristic
287C22×C73#46811yescharacteristic
288C22×C73#46911yescharacteristic
289C22×C73#46911yescharacteristic
290C22×C73#47011yescharacteristic
291C22×C73#47011yescharacteristic
292C22×C73#48911yescharacteristic
293C22×C73#48911yescharacteristic
294C22×C73#49011yescharacteristic
295C22×C73#49111yescharacteristic
296C22×C73#50111yescharacteristic
297C22×C73#50111yescharacteristic
298C22×C73#50111yescharacteristic
299C22×C73#50111yescharacteristic
300C4×C73—44no—
301C4×C73—82no—
302C4×C73C4×C4⋊C411yescharacteristic
303C4×C73C4×C4⋊C411yescharacteristic
304C4×C73#38511yescharacteristic
305C4×C73#38511yescharacteristic
306C4×C73#38711yescharacteristic
307C4×C73#38711yescharacteristic
308C4×C73#38711yescharacteristic
309C4×C73#38711yescharacteristic
310Dic73—42no—
311Dic73—42no—
312Dic73—82no—
313Dic73—82no—
314#10881—731nomaximal, Sylow
315C2×C73#143611yescharacteristic
316C2×C73#176211yescharacteristic
317C2×C73#176311yescharacteristic
318C2×C73#189411yescharacteristic
319C2×C73#189511yescharacteristic
320C2×C73#193511yescharacteristic
321C2×C73#193511yescharacteristic
322C2×C73#193611yescharacteristic
323C2×C73#193611yescharacteristic
324C2×C73#194311yescharacteristic
325C2×C73#194311yescharacteristic
326C2×C73#194411yescharacteristic
327C2×C73#194411yescharacteristic
328C2×C73#199211yescharacteristic
329C2×C73#199311yescharacteristic
330C22×#97—731no—
331C2×#389—731no—
332C2×#340—731no—
333C2×#340—731no—
334C2×#340—731no—
335C2×#340D7311yescharacteristic
336C4⋊#95—731no—
337C73#1088111yescharacteristic, complemented, Sylow
338C23×C8—731no—
339C23×C8C2×D7311yescharacteristic
340C22×C4⋊C4—731no—
341C22×C4⋊C4—731no—
342C22×C4⋊C4—1461no—
343C22×C4⋊C4C2×D7311yescharacteristic
344C22×C4⋊C4C2×D7311yescharacteristic
345C22×C42—731no—
346C2×#97—1462no—
347C2×#97—1462no—
348C2×#97—1462no—
349#389—734no—
350#389—1462no—
351C2×#95—1461no—
352C2×#95—1461no—
353C2×#95—1461no—
354#340—734no—
355#340—1462no—
356#340—1462no—
357#340Dic7314yescomplemented
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—731no—
361C23×C4—731no—
362C23×C4—1461no—
363C23×C4—1461no—
364C23×C4C22×D7311yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—732no—
370C22×C8—732no—
371C22×C8—732no—
372C22×C8—1461no—
373C22×C8—1461no—
374C22×C8—1461no—
375C22×C8—1461no—
376C22×C8Dic14612yes—
377C22×C8D29212yes—
378C22×C8C2×Dic7312yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—2922no—
388C2×C4⋊C4—2922no—
389C2×C4⋊C4—732no—
390C2×C4⋊C4—732no—
391C2×C4⋊C4—1464no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4—1461no—
396C2×C4⋊C4—1461no—
397C2×C4⋊C4—1461no—
398C2×C4⋊C4—1461no—
399C2×C4⋊C4—1461no—
400C2×C4⋊C4—1461no—
401C2×C4⋊C4—1461no—
402C2×C4⋊C4C4×D7312yes—
403C2×C4⋊C4C4×D7312yes—
404C2×C4⋊C4C2×Dic7312yes—
405C2×C4⋊C4C2×Dic7312yes—
406C2×C42—732no—
407C2×C42—732no—
408C2×C42—1461no—
409C2×C42—1461no—
410C2×C42—1461no—
411C2×C42—1461no—
412#97—1468no—
413#95—2922no—
414#95—2922no—
415#95—1464no—
416C24D4×D7311yescharacteristic
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—2921no—
432C22×C4—2921no—
433C22×C4—2921no—
434C22×C4—2921no—
435C22×C4—2921no—
436C22×C4—2921no—
437C22×C4—2921no—
438C22×C4—2921no—
439C22×C4—2921no—
440C22×C4—2921no—
441C22×C4—2921no—
442C22×C4—2921no—
443C22×C4—732no—
444C22×C4—732no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4—1461no—
452C22×C4—1461no—
453C22×C4—1461no—
454C22×C4—1461no—
455C22×C4—1461no—
456C22×C4—1461no—
457C22×C4—1461no—
458C22×C4—1461no—
459C22×C4C2×C4×D7311yescharacteristic
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C22×Dic7311yescharacteristic
462C22×C4D4×D7311yescharacteristic
463C22×C4D4×D7311yescharacteristic
464C22×C4C2×D29211yescharacteristic
465C22×C4Q8×D7311yescharacteristic
466C22×C4C2×Dic14611yescharacteristic
467C22×C4#1192402711yescharacteristic
468C22×C4#1192402711yescharacteristic
469C22×C4#1192402711yescharacteristic
470C22×C4#1192402811yescharacteristic
471C22×C4#1192402811yescharacteristic
472C22×C4#1192402911yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—734no—
480C2×C8—1462no—
481C2×C8—1462no—
482C2×C8—1462no—
483C2×C8—1462no—
484C2×C8—1462no—
485C2×C8—1462no—
486C2×C8C4⋊Dic7314yescomplemented
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—2928no—
495C4⋊C4—2921no—
496C4⋊C4—2921no—
497C4⋊C4—2921no—
498C4⋊C4—2921no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4—1462no—
502C4⋊C4—1462no—
503C4⋊C4C4×Dic7314yes—
504C42—1462no—
505C42—1462no—
506C42—1462no—
507C42—1462no—
508C23C22⋊C4×D7311yescharacteristic
509C23#1455655111yescharacteristic
510C23D4×Dic7311yescharacteristic
511C23#1455656411yescharacteristic
512C23#1455656611yescharacteristic
513C23#1455657711yescharacteristic
514C23#1455659011yescharacteristic
515C23#1455661511yescharacteristic
516C23#1455661511yescharacteristic
517C23#1455661811yescharacteristic
518C23#1455661811yescharacteristic
519C23#1455662011yescharacteristic
520C23#1455662011yescharacteristic
521C23#1455662311yescharacteristic
522C23#1455662311yescharacteristic
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—2922no—
546C2×C4—2922no—
547C2×C4—2922no—
548C2×C4—2922no—
549C2×C4—2922no—
550C2×C4—2922no—
551C2×C4—5841no—
552C2×C4—5841no—
553C2×C4—5841no—
554C2×C4—5841no—
555C2×C4—5841no—
556C2×C4—5841no—
557C2×C4—5841no—
558C2×C4—5841no—
559C2×C4—1462no—
560C2×C4—1462no—
561C2×C4—1462no—
562C2×C4—1462no—
563C2×C4—1462no—
564C2×C4—1462no—
565C2×C4C2×C4×Dic7311yescharacteristic
566C2×C4C4⋊C4×D7311yescharacteristic
567C2×C4C2×C4⋊Dic7311yescharacteristic
568C2×C4#1455654711yescharacteristic
569C2×C4#1455654911yescharacteristic
570C2×C4#1455655011yescharacteristic
571C2×C4#1455655111yescharacteristic
572C2×C4#1455655311yescharacteristic
573C2×C4D4×Dic7311yescharacteristic
574C2×C4D4×Dic7311yescharacteristic
575C2×C4C4×D29211yescharacteristic
576C2×C4C4×D29211yescharacteristic
577C2×C4#1455655611yescharacteristic
578C2×C4C4×Dic14611yescharacteristic
579C2×C4C4×Dic14611yescharacteristic
580C2×C4Q8×Dic7311yescharacteristic
581C2×C4#1455656111yescharacteristic
582C2×C4#1455656811yescharacteristic
583C2×C4#1455656811yescharacteristic
584C2×C4#1455656911yescharacteristic
585C2×C4#1455657111yescharacteristic
586C2×C4#1455657311yescharacteristic
587C2×C4#1455657511yescharacteristic
588C2×C4#1455657611yescharacteristic
589C2×C4#1455658111yescharacteristic
590C2×C4#1455658211yescharacteristic
591C2×C4#1455658411yescharacteristic
592C2×C4#1455658611yescharacteristic
593C8—24no—
594C8—1464no—
595C22C22⋊C4×Dic7311yescharacteristic
596C22#1798846511yescharacteristic
597C22#1798847911yescharacteristic
598C22#1798848011yescharacteristic
599C22#1798848411yescharacteristic
600C22#1798848611yescharacteristic
601C22#1798849111yescharacteristic
602C22#1798858511yescharacteristic
603C22#1798858711yescharacteristic
604C22#1798859011yescharacteristic
605C22#1798859411yescharacteristic
606C22#1798868411yescharacteristic
607C22#1798868811yescharacteristic
608C22#1798868811yescharacteristic
609C22#1798869011yescharacteristic
610C22#1798869111yescharacteristic
611C22#1798869411yescharacteristic
612C22#1798869611yescharacteristic
613C22#1798869911yescharacteristic
614C22#1798883211yescharacteristic
615C22#1798883411yescharacteristic
616C22#1798883411yescharacteristic
617C22#1798883611yescharacteristic
618C22#1798883911yescharacteristic
619C22#1798884111yescharacteristic
620C22#1798884411yescharacteristic
621C22#1798884611yescharacteristic
622C22#1798894511yescharacteristic
623C22#1798894811yescharacteristic
624C22#1798895011yescharacteristic
625C22#1798895411yescharacteristic
626C22#1798899411yescharacteristic
627C22#1798899411yescharacteristic
628C22#1798899511yescharacteristic
629C22#1798899511yescharacteristic
630C4—44no—
631C4—82no—
632C4—2922no—
633C4—2922no—
634C4—5842no—
635C4—5842no—
636C4C4×C4⋊Dic7311yescharacteristic
637C4C4⋊C4×Dic7311yescharacteristic
638C4#1798846111yescharacteristic
639C4#1798846211yescharacteristic
640C4#1798847011yescharacteristic
641C4#1798847211yescharacteristic
642C4#1798847311yescharacteristic
643C4#1798847411yescharacteristic
644C2#2260816511yescharacteristic
645C2#2260975811yescharacteristic
646C2#2260976311yescharacteristic
647C2#2261036311yescharacteristic
648C2#2261036811yescharacteristic
649C2#2261062211yescharacteristic
650C2#2261062311yescharacteristic
651C2#2261062911yescharacteristic
652C2#2261063011yescharacteristic
653C2#2261066811yescharacteristic
654C2#2261067011yescharacteristic
655C2#2261067311yescharacteristic
656C2#2261067511yescharacteristic
657C2#2261089811yescharacteristic
658C2#2261090211yescharacteristic
subgroupG/H
centerC24D4×D73
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC2×#340×C73C2
socle, prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenterC2×#340D73
hypocenterC73#10881
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
17. #17988486C4semidirect
23. #17988349C4semidirect
27. #340×C73C4semidirect
120. C2×#10596831C4⋊C4semidirect
169. C2×C8×C73C4⋊C4semidirect
337. C73#10881semidirect
357. #340Dic73semidirect
486. C2×C8C4⋊Dic73semidirect

Maximal subgroups

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

subgroupindex
C22×#145565012
C2×#179884862
C2×#179883502
C2×#179883492
#226081602
C2×#340×C732
#1088173