Finite Group Databasebeta

← #32994612

Subgroups — #32994612

Order 18688.

958 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556522C211yesmaximal, characteristic
2C2×#17988485C211yesmaximal, characteristic
3C2×#17988349C211yesmaximal, characteristic
4C2×#17988349C211yesmaximal, characteristic
5C2×#17988349C211yesmaximal, characteristic
6C2×#17988342C211yesmaximal, characteristic
7C2×#389×C73C211yesmaximal, characteristic
8C23×#10596831C2211yescharacteristic
9C23×#10596831C2211yescharacteristic
10C22×C4⋊Dic73C2211yescharacteristic
11C22×C4⋊Dic73C2211yescharacteristic
12C22×#11924007—21no—
13C2×#14556522—22no—
14C2×#14556522—22no—
15C2×#14556522—22no—
16#17988485—22no—
17#17988485—22no—
18C2×#14556498—21no—
19#17988349—22no—
20#17988349—22no—
21#17988349C414yescomplemented
22#17988342—22no—
23C22×C4⋊C4×C73—21no—
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C22×C42×C73C2211yescharacteristic
27#389×C73—22no—
28#389×C73—22no—
29C2×#95×C73—21no—
30C23×Dic73—21no—
31C23×Dic73—21no—
32C22×#10596831—21no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35C22×#10596831—21no—
36C22×#10596831—21no—
37C22×#10596831—21no—
38C22×#10596831—21no—
39C22×#10596831—21no—
40C22×#10596831—21no—
41C22×#10596831—21no—
42C22×#10596831C2×C412yes—
43C22×#10596831D412yes—
44C22×#10596831Q812yes—
45C22×#10596831Q812yes—
46C2×C4⋊Dic73—21no—
47C2×C4⋊Dic73—21no—
48C2×C4⋊Dic73—21no—
49C2×C4⋊Dic73—21no—
50C2×C4⋊Dic73—21no—
51C2×C4⋊Dic73—21no—
52C2×C4⋊Dic73—21no—
53C2×C4⋊Dic73—21no—
54C2×C4⋊Dic73C2×C412yes—
55C2×C4⋊Dic73D412yes—
56C2×C4⋊Dic73D412yes—
57C2×C4⋊Dic73Q812yes—
58C2×#11924007—24no—
59C2×#11924007—42no—
60C2×#11924007—42no—
61#14556522—28no—
62#14556498—24no—
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73D411yescharacteristic
66C23×C4×C73D411yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C2×C4⋊C4×C73—21no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—24no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73—42no—
78C2×C4⋊C4×C73—42no—
79C2×C4⋊C4×C73C2×C412yes—
80C2×C4⋊C4×C73D412yes—
81C2×C4⋊C4×C73D412yes—
82C2×C4⋊C4×C73Q812yes—
83C2×C42×C73—21no—
84C2×C42×C73—21no—
85C2×C42×C73—21no—
86C2×C42×C73—21no—
87C2×C42×C73—21no—
88C2×C42×C73—21no—
89#95×C73—24no—
90C22×Dic73—22no—
91C22×Dic73—22no—
92C22×Dic73—22no—
93C22×Dic73—22no—
94C22×Dic73—41no—
95C22×Dic73—41no—
96C22×Dic73—41no—
97C22×Dic73—41no—
98C22×Dic73—41no—
99C22×Dic73—41no—
100C22×Dic73—41no—
101C22×Dic73—41no—
102C22×Dic73—41no—
103C22×Dic73—41no—
104C2×#10596831—22no—
105C2×#10596831—22no—
106C2×#10596831—22no—
107C2×#10596831—22no—
108C2×#10596831—22no—
109C2×#10596831—22no—
110C2×#10596831—22no—
111C2×#10596831—22no—
112C2×#10596831—22no—
113C2×#10596831—41no—
114C2×#10596831—41no—
115C2×#10596831—41no—
116C2×#10596831—41no—
117C2×#10596831C4⋊C414yescomplemented
118C4⋊Dic73—22no—
119C4⋊Dic73—22no—
120C4⋊Dic73—22no—
121C4⋊Dic73—22no—
122C4⋊Dic73—22no—
123C4⋊Dic73—41no—
124C4⋊Dic73—41no—
125C4⋊Dic73C4⋊C414yescomplemented
126#11924007—48no—
127C24×C73C2×D411yescharacteristic
128C22×C4×C73—22no—
129C22×C4×C73—21no—
130C22×C4×C73—22no—
131C22×C4×C73—21no—
132C22×C4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—22no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—22no—
144C22×C4×C73—41no—
145C22×C4×C73—41no—
146C22×C4×C73—41no—
147C22×C4×C73—41no—
148C22×C4×C73—41no—
149C22×C4×C73—41no—
150C22×C4×C73—41no—
151C22×C4×C73—41no—
152C22×C4×C73—41no—
153C22×C4×C73—41no—
154C22×C4×C73SD1612yes—
155C22×C4×C73SD1612yes—
156C22×C4×C73C22×C411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73C2×D411yescharacteristic
159C22×C4×C73C2×D411yescharacteristic
160C22×C4×C73C2×D411yescharacteristic
161C22×C4×C73C2×D411yescharacteristic
162C22×C4×C73C2×Q811yescharacteristic
163C22×C4×C73C2×Q811yescharacteristic
164C22×C4×C73C2×Q811yescharacteristic
165C22×C4×C73C2×Q811yescharacteristic
166C22×C4×C73#4111yescharacteristic
167C22×C4×C73#4111yescharacteristic
168C22×C4×C73#4111yescharacteristic
169C22×C4×C73#4111yescharacteristic
170C4⋊C4×C73—22no—
171C4⋊C4×C73—22no—
172C4⋊C4×C73—22no—
173C4⋊C4×C73—22no—
174C4⋊C4×C73—22no—
175C4⋊C4×C73—48no—
176C4⋊C4×C73—41no—
177C4⋊C4×C73—41no—
178C4⋊C4×C73C4⋊C414yescomplemented
179C42×C73—41no—
180C42×C73—41no—
181C42×C73—41no—
182C42×C73—41no—
183C23×C73C4×D411yescharacteristic
184C23×C73#12011yescharacteristic
185C23×C73#12011yescharacteristic
186C23×C73#12111yescharacteristic
187C23×C73C22⋊Q811yescharacteristic
188C23×C73C22⋊Q811yescharacteristic
189C23×C73C4⋊Q811yescharacteristic
190C23×C73C2×SD1611yescharacteristic
191C23×C73C2×SD1611yescharacteristic
192C23×C73#13511yescharacteristic
193C23×C73#13511yescharacteristic
194C23×C73AGL(1,ℤ/8)11yescharacteristic
195C23×C73AGL(1,ℤ/8)11yescharacteristic
196C23×C73#13711yescharacteristic
197C23×C73#13711yescharacteristic
198C2×C4×C73—24no—
199C2×C4×C73—22no—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—41no—
206C2×C4×C73—41no—
207C2×C4×C73—42no—
208C2×C4×C73—42no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—42no—
212C2×C4×C73—42no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—81no—
223C2×C4×C73—81no—
224C2×C4×C73—81no—
225C2×C4×C73—81no—
226C2×C4×C73C2×C4⋊C411yescharacteristic
227C2×C4×C73C2×C4⋊C411yescharacteristic
228C2×C4×C73C2×C4⋊C411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×Q811yescharacteristic
232C2×C4×C73#12011yescharacteristic
233C2×C4×C73#12111yescharacteristic
234C2×C4×C73#12111yescharacteristic
235C2×C4×C73C22⋊Q811yescharacteristic
236C2×C4×C73C22⋊Q811yescharacteristic
237C2×C4×C73C22⋊Q811yescharacteristic
238C2×C4×C73C22⋊Q811yescharacteristic
239C2×C4×C73C22⋊Q811yescharacteristic
240C2×C4×C73C22⋊Q811yescharacteristic
241C2×C4×C73C22⋊Q811yescharacteristic
242C2×C4×C73#12311yescharacteristic
243C2×C4×C73#12311yescharacteristic
244C2×C4×C73#12311yescharacteristic
245C2×C4×C73#12511yescharacteristic
246C2×C4×C73#12511yescharacteristic
247C2×C4×C73#12511yescharacteristic
248C2×C4×C73#12711yescharacteristic
249C2×C4×C73C4⋊Q811yescharacteristic
250C2×C4×C73C4⋊Q811yescharacteristic
251C2×C4×C73C4⋊Q811yescharacteristic
252C2×C4×C73C4⋊Q811yescharacteristic
253C2×C4×C73C4⋊Q811yescharacteristic
254C2×Dic73—24no—
255C2×Dic73—42no—
256C2×Dic73—42no—
257C2×Dic73—42no—
258C2×Dic73—42no—
259C2×Dic73—42no—
260C2×Dic73—42no—
261C2×Dic73—42no—
262C2×Dic73—42no—
263C2×Dic73—42no—
264C2×Dic73—81no—
265C2×Dic73—81no—
266C2×Dic73—81no—
267C2×Dic73—81no—
268#10596831—24no—
269#10596831—42no—
270C22×C73#38511yescharacteristic
271C22×C73#38511yescharacteristic
272C22×C73#38911yescharacteristic
273C22×C73#39211yescharacteristic
274C22×C73#39511yescharacteristic
275C22×C73#39511yescharacteristic
276C22×C73#39811yescharacteristic
277C22×C73C4×SD1611yescharacteristic
278C22×C73C4×SD1611yescharacteristic
279C22×C73#44111yescharacteristic
280C22×C73#44211yescharacteristic
281C22×C73#44811yescharacteristic
282C22×C73#44811yescharacteristic
283C22×C73#44911yescharacteristic
284C22×C73#44911yescharacteristic
285C22×C73#45011yescharacteristic
286C22×C73#45011yescharacteristic
287C22×C73#45211yescharacteristic
288C22×C73#45211yescharacteristic
289C22×C73#46511yescharacteristic
290C22×C73#46511yescharacteristic
291C22×C73#46811yescharacteristic
292C22×C73#46811yescharacteristic
293C22×C73#47511yescharacteristic
294C22×C73#47511yescharacteristic
295C22×C73#47611yescharacteristic
296C22×C73#47611yescharacteristic
297C22×C73#47811yescharacteristic
298C22×C73#47811yescharacteristic
299C22×C73#47911yescharacteristic
300C22×C73#47911yescharacteristic
301C22×C73#49811yescharacteristic
302C22×C73#49911yescharacteristic
303C22×C73#50111yescharacteristic
304C22×C73#50111yescharacteristic
305C4×C73—44no—
306C4×C73—42no—
307C4×C73—42no—
308C4×C73—82no—
309C4×C73#38411yescharacteristic
310C4×C73#38511yescharacteristic
311C4×C73#38911yescharacteristic
312C4×C73#38911yescharacteristic
313C4×C73#39511yescharacteristic
314C4×C73#39811yescharacteristic
315C4×C73#39811yescharacteristic
316C4×C73#39911yescharacteristic
317Dic73—44no—
318Dic73—82no—
319#11327—731nomaximal, Sylow
320C2×C73#144411yescharacteristic
321C2×C73#186411yescharacteristic
322C2×C73#186411yescharacteristic
323C2×C73#186511yescharacteristic
324C2×C73#186511yescharacteristic
325C2×C73#194111yescharacteristic
326C2×C73#194311yescharacteristic
327C2×C73#200011yescharacteristic
328C2×C73#200011yescharacteristic
329C2×C73#205811yescharacteristic
330C2×C73#205811yescharacteristic
331C2×C73#205911yescharacteristic
332C2×C73#205911yescharacteristic
333C2×C73#208811yescharacteristic
334C2×C73#208811yescharacteristic
335C22×#106—731no—
336C2×#389—731no—
337C2×#389D7311yescharacteristic
338C2×#340—731no—
339C2×#340—731no—
340C2×#340—731no—
341C2×#336—731no—
342C73#1132711yescharacteristic, complemented, Sylow
343C23×C8—731no—
344C23×C8—731no—
345C22×C4⋊C4—21no—
346C22×C4⋊C4—731no—
347C22×C4⋊C4—731no—
348C22×C4⋊C4—1461no—
349C22×C4⋊C4C2×D7311yescharacteristic
350C22×C4⋊C4C2×D7311yescharacteristic
351C22×C42C2×D7311yescharacteristic
352C2×#106—1462no—
353C2×#106—1462no—
354C2×#106—1462no—
355#389—22no—
356#389—22no—
357#389—1462no—
358#389—1462no—
359C2×#95—21no—
360C2×#95—1461no—
361#340—734no—
362#340—1462no—
363#340—1462no—
364#336—1462no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—1461no—
368C23×C4—1461no—
369C23×C4C22⋊D7311yescharacteristic
370C23×C4C22⋊D7311yescharacteristic
371C23×C4C22×D7311yescharacteristic
372C22×C8—732no—
373C22×C8—732no—
374C22×C8—732no—
375C22×C8—732no—
376C22×C8—1461no—
377C22×C8—1461no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C22×C8—1461no—
384C22×C8—1461no—
385C22×C8—1461no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—2922no—
398C2×C4⋊C4—2922no—
399C2×C4⋊C4—732no—
400C2×C4⋊C4—732no—
401C2×C4⋊C4—732no—
402C2×C4⋊C4—732no—
403C2×C4⋊C4—1464no—
404C2×C4⋊C4—1461no—
405C2×C4⋊C4—1461no—
406C2×C4⋊C4—1461no—
407C2×C4⋊C4—1461no—
408C2×C4⋊C4—1461no—
409C2×C4⋊C4—1461no—
410C2×C4⋊C4—1461no—
411C2×C4⋊C4—1461no—
412C2×C4⋊C4Dic14612yes—
413C2×C4⋊C4C4×D7312yes—
414C2×C4⋊C4C22⋊D7312yes—
415C2×C4⋊C4C22⋊D7312yes—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422#106—1468no—
423#95—24no—
424#95—1464no—
425C24C2×C22⋊D7311yescharacteristic
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—2921no—
453C22×C4—2921no—
454C22×C4—2921no—
455C22×C4—2921no—
456C22×C4—2921no—
457C22×C4—2921no—
458C22×C4—2921no—
459C22×C4—2921no—
460C22×C4—2921no—
461C22×C4—2921no—
462C22×C4—1462no—
463C22×C4—1462no—
464C22×C4—1462no—
465C22×C4—1462no—
466C22×C4#1192401512yes—
467C22×C4#1192401612yes—
468C22×C4C2×C4×D7311yescharacteristic
469C22×C4D4×D7311yescharacteristic
470C22×C4D4×D7311yescharacteristic
471C22×C4D4×D7311yescharacteristic
472C22×C4C2×C22⋊D7311yescharacteristic
473C22×C4C2×C22⋊D7311yescharacteristic
474C22×C4Q8×D7311yescharacteristic
475C22×C4Q8×D7311yescharacteristic
476C22×C4Q8×D7311yescharacteristic
477C22×C4C2×Dic14611yescharacteristic
478C22×C4#1192402711yescharacteristic
479C22×C4#1192402811yescharacteristic
480C22×C4#1192402811yescharacteristic
481C22×C4#1192402911yescharacteristic
482C2×C8—2921no—
483C2×C8—2921no—
484C2×C8—2921no—
485C2×C8—2921no—
486C2×C8—734no—
487C2×C8—1462no—
488C2×C8—1462no—
489C2×C8—1462no—
490C2×C8—1462no—
491C2×C8—1462no—
492C2×C8—1462no—
493C2×C8—1462no—
494C2×C8—1462no—
495C2×C8—1462no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—48no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—2928no—
505C4⋊C4—2921no—
506C4⋊C4—2921no—
507C4⋊C4—734no—
508C4⋊C4—1462no—
509C4⋊C4—1462no—
510C4⋊C4—1462no—
511C4⋊C4—1462no—
512C4⋊C4—1462no—
513C4⋊C4#1192400714yescomplemented
514C42—41no—
515C42—41no—
516C42—41no—
517C42—41no—
518C23C4×C22⋊D7311yescharacteristic
519C23#1455655911yescharacteristic
520C23#1455656011yescharacteristic
521C23#1455656311yescharacteristic
522C23#1455656711yescharacteristic
523C23#1455657011yescharacteristic
524C23#1455658911yescharacteristic
525C23C2×#1192401511yescharacteristic
526C23C2×#1192401611yescharacteristic
527C23#1455661111yescharacteristic
528C23#1455661111yescharacteristic
529C23#1455661611yescharacteristic
530C23#1455661711yescharacteristic
531C23#1455662111yescharacteristic
532C23#1455662211yescharacteristic
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—2922no—
562C2×C4—2922no—
563C2×C4—2922no—
564C2×C4—2922no—
565C2×C4—2922no—
566C2×C4—2922no—
567C2×C4—2922no—
568C2×C4—2922no—
569C2×C4—2922no—
570C2×C4—5841no—
571C2×C4—5841no—
572C2×C4—5841no—
573C2×C4—5841no—
574C2×C4—1464no—
575C2×C4C4⋊C4×D7311yescharacteristic
576C2×C4C4⋊C4×D7311yescharacteristic
577C2×C4C2×#1192400711yescharacteristic
578C2×C4C4×C22⋊D7311yescharacteristic
579C2×C4#1455655311yescharacteristic
580C2×C4#1455655611yescharacteristic
581C2×C4#1455655911yescharacteristic
582C2×C4#1455656211yescharacteristic
583C2×C4#1455656311yescharacteristic
584C2×C4#1455656711yescharacteristic
585C2×C4#1455656711yescharacteristic
586C2×C4#1455656911yescharacteristic
587C2×C4#1455656911yescharacteristic
588C2×C4#1455656911yescharacteristic
589C2×C4#1455656911yescharacteristic
590C2×C4#1455657011yescharacteristic
591C2×C4#1455657411yescharacteristic
592C2×C4#1455657611yescharacteristic
593C2×C4#1455657611yescharacteristic
594C2×C4#1455658111yescharacteristic
595C2×C4#1455658111yescharacteristic
596C2×C4#1455658211yescharacteristic
597C2×C4#1455658711yescharacteristic
598C2×C4#1455658911yescharacteristic
599C2×C4#1455658911yescharacteristic
600C2×C4#1455659011yescharacteristic
601C2×C4#1455659011yescharacteristic
602C2×C4#1455659011yescharacteristic
603C8—2922no—
604C8—1464no—
605C22#1798845811yescharacteristic
606C22#1798846011yescharacteristic
607C22#1798848211yescharacteristic
608C22#1798849511yescharacteristic
609C22#1798850611yescharacteristic
610C22#1798850711yescharacteristic
611C22#1798852011yescharacteristic
612C22C4×#1192401611yescharacteristic
613C22C4×#1192401511yescharacteristic
614C22#1798869211yescharacteristic
615C22#1798869711yescharacteristic
616C22#1798872511yescharacteristic
617C22#1798872611yescharacteristic
618C22#1798873011yescharacteristic
619C22#1798873211yescharacteristic
620C22#1798873711yescharacteristic
621C22#1798873811yescharacteristic
622C22#1798874711yescharacteristic
623C22#1798874911yescharacteristic
624C22#1798881411yescharacteristic
625C22#1798881811yescharacteristic
626C22#1798883111yescharacteristic
627C22#1798883511yescharacteristic
628C22#1798886911yescharacteristic
629C22#1798887211yescharacteristic
630C22#1798887411yescharacteristic
631C22#1798887711yescharacteristic
632C22#1798888411yescharacteristic
633C22#1798888711yescharacteristic
634C22#1798889111yescharacteristic
635C22#1798889411yescharacteristic
636C22#1798898311yescharacteristic
637C22#1798898611yescharacteristic
638C22#1798899311yescharacteristic
639C22#1798899711yescharacteristic
640C4—44no—
641C4—42no—
642C4—42no—
643C4—82no—
644C4—2924no—
645C4—5842no—
646C4#1798845611yescharacteristic
647C4#1798845811yescharacteristic
648C4#1798848211yescharacteristic
649C4#1798848311yescharacteristic
650C4#1798850711yescharacteristic
651C4#1798851811yescharacteristic
652C4#1798852011yescharacteristic
653C4#1798852211yescharacteristic
654C2#2260819411yescharacteristic
655C2#2261019111yescharacteristic
656C2#2261019211yescharacteristic
657C2#2261019811yescharacteristic
658C2#2261019911yescharacteristic
659C2#2261065611yescharacteristic
660C2#2261066611yescharacteristic
661C2#2261093211yescharacteristic
662C2#2261093411yescharacteristic
663C2#2261126111yescharacteristic
664C2#2261126411yescharacteristic
665C2#2261126611yescharacteristic
666C2#2261126911yescharacteristic
667C2#2261143211yescharacteristic
668C2#2261143311yescharacteristic
subgroupG/H
centerC24C2×C22⋊D73
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC2×#389×C73C2
socle, prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenterC2×#389D73
hypocenterC73#11327
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
21. #17988349C4semidirect
117. C2×#10596831C4⋊C4semidirect
125. C4⋊Dic73C4⋊C4semidirect
178. C4⋊C4×C73C4⋊C4semidirect
342. C73#11327semidirect
513. C4⋊C4#11924007semidirect

Maximal subgroups

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

subgroupindex
C22×#145565222
C2×#179884852
C2×#179883492
C2×#179883422
C2×#389×C732
#1132773