Finite Group Databasebeta

← #32992149

Subgroups — #32992149

Order 18688.

958 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×#14556522C211yesmaximal, characteristic
2C2×#17988349C211yesmaximal, characteristic
3C2×#17988349C211yesmaximal, characteristic
4C2×#17988349C211yesmaximal, characteristic
5C2×#17988342C211yesmaximal, characteristic
6#22608161C211yesmaximal, characteristic
7C2×C4×C4⋊C4×C73C211yesmaximal, characteristic
8C23×#10596831C2211yescharacteristic
9C23×#10596831C2211yescharacteristic
10C22×C4⋊Dic73C2211yescharacteristic
11C22×C4⋊Dic73C2211yescharacteristic
12C2×#14556522—22no—
13C2×#14556522—22no—
14C2×#14556522C414yescomplemented
15C2×#14556498—21no—
16C2×#14556498—21no—
17#17988349—22no—
18#17988349—22no—
19#17988349C414yescomplemented
20#17988342C414yescomplemented
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C42×C73—21no—
24C22×C42×C73C2211yescharacteristic
25C4×C4⋊C4×C73—22no—
26C4×C4⋊C4×C73—22no—
27C2×#95×C73—21no—
28C23×Dic73—21no—
29C23×Dic73—21no—
30C22×#10596831—21no—
31C22×#10596831—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×#10596831C2×C412yes—
41C22×#10596831C2×C412yes—
42C22×#10596831C2×C412yes—
43C22×#10596831C2×C412yes—
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—21no—
51C2×C4⋊Dic73—21no—
52C2×C4⋊Dic73—21no—
53C2×C4⋊Dic73—21no—
54C2×C4⋊Dic73C2×C412yes—
55C2×C4⋊Dic73C2×C412yes—
56#14556522—28no—
57#14556498—42no—
58#14556498—42no—
59C23×C4×C73—21no—
60C23×C4×C73—21no—
61C23×C4×C73D411yescharacteristic
62C23×C4×C73D411yescharacteristic
63C23×C4×C73C2311yescharacteristic
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—21no—
66C2×C4⋊C4×C73—21no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73—21no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73C2×C412yes—
71C2×C4⋊C4×C73C2×C412yes—
72C2×C4⋊C4×C73D412yes—
73C2×C4⋊C4×C73D412yes—
74C2×C4⋊C4×C73D412yes—
75C2×C4⋊C4×C73Q812yes—
76C2×C42×C73—21no—
77C2×C42×C73—21no—
78C2×C42×C73—21no—
79C2×C42×C73—21no—
80C2×C42×C73—24no—
81C2×C42×C73—42no—
82C2×C42×C73—42no—
83C2×C42×C73C2×C412yes—
84C2×C42×C73Q812yes—
85#95×C73—24no—
86C22×Dic73—22no—
87C22×Dic73—22no—
88C22×Dic73—41no—
89C22×Dic73—41no—
90C22×Dic73—41no—
91C22×Dic73—41no—
92C22×Dic73—41no—
93C22×Dic73—41no—
94C22×Dic73—41no—
95C22×Dic73—41no—
96C22×Dic73—41no—
97C22×Dic73—41no—
98C22×Dic73—41no—
99C22×Dic73—41no—
100C2×#10596831—22no—
101C2×#10596831—22no—
102C2×#10596831—22no—
103C2×#10596831—22no—
104C2×#10596831—22no—
105C2×#10596831—22no—
106C2×#10596831—22no—
107C2×#10596831—22no—
108C2×#10596831—22no—
109C2×#10596831—41no—
110C2×#10596831—41no—
111C2×#10596831—41no—
112C2×#10596831—41no—
113C2×#10596831C4214yescomplemented
114C4⋊Dic73—22no—
115C4⋊Dic73—22no—
116C4⋊Dic73—22no—
117C4⋊Dic73—22no—
118C4⋊Dic73—41no—
119C4⋊Dic73—41no—
120C4⋊Dic73—41no—
121C4⋊Dic73—41no—
122C24×C73C2×D411yescharacteristic
123C22×C4×C73—21no—
124C22×C4×C73—21no—
125C22×C4×C73—21no—
126C22×C4×C73—21no—
127C22×C4×C73—22no—
128C22×C4×C73—22no—
129C22×C4×C73—21no—
130C22×C4×C73—22no—
131C22×C4×C73—22no—
132C22×C4×C73—22no—
133C22×C4×C73—22no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
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×C73C4⋊C412yes—
148C22×C4×C73C4⋊C412yes—
149C22×C4×C73SD1612yes—
150C22×C4×C73SD1612yes—
151C22×C4×C73C22×C411yescharacteristic
152C22×C4×C73C22×C411yescharacteristic
153C22×C4×C73C22×C411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155C22×C4×C73C2×D411yescharacteristic
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73C2×Q811yescharacteristic
158C22×C4×C73C2×Q811yescharacteristic
159C22×C4×C73#4111yescharacteristic
160C22×C4×C73#4111yescharacteristic
161C22×C4×C73#4111yescharacteristic
162C22×C4×C73#4111yescharacteristic
163C22×C4×C73#4111yescharacteristic
164C22×C4×C73#4111yescharacteristic
165C4⋊C4×C73—22no—
166C4⋊C4×C73—22no—
167C4⋊C4×C73—22no—
168C4⋊C4×C73—22no—
169C4⋊C4×C73—22no—
170C4⋊C4×C73—22no—
171C4⋊C4×C73C22⋊C414yes—
172C4⋊C4×C73C4⋊C414yes—
173C42×C73—22no—
174C42×C73—22no—
175C42×C73—22no—
176C42×C73—22no—
177C42×C73—48no—
178C23×C73C2×C4⋊C411yescharacteristic
179C23×C73C4×D411yescharacteristic
180C23×C73C4×D411yescharacteristic
181C23×C73#12011yescharacteristic
182C23×C73#12111yescharacteristic
183C23×C73C22⋊Q811yescharacteristic
184C23×C73#12311yescharacteristic
185C23×C73C2×SD1611yescharacteristic
186C23×C73C2×SD1611yescharacteristic
187C23×C73#13511yescharacteristic
188C23×C73#13511yescharacteristic
189C23×C73AGL(1,ℤ/8)11yescharacteristic
190C23×C73AGL(1,ℤ/8)11yescharacteristic
191C23×C73#13711yescharacteristic
192C23×C73#13711yescharacteristic
193C2×C4×C73—22no—
194C2×C4×C73—22no—
195C2×C4×C73—22no—
196C2×C4×C73—22no—
197C2×C4×C73—22no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—24no—
201C2×C4×C73—24no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—42no—
205C2×C4×C73—42no—
206C2×C4×C73—42no—
207C2×C4×C73—42no—
208C2×C4×C73—41no—
209C2×C4×C73—42no—
210C2×C4×C73—42no—
211C2×C4×C73—42no—
212C2×C4×C73—41no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73#10614yescomplemented
221C2×C4×C73C2×C4211yescharacteristic
222C2×C4×C73C2×C22⋊C411yescharacteristic
223C2×C4×C73C2×C4⋊C411yescharacteristic
224C2×C4×C73#11711yescharacteristic
225C2×C4×C73#11711yescharacteristic
226C2×C4×C73#11711yescharacteristic
227C2×C4×C73C4×D411yescharacteristic
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C4×D411yescharacteristic
230C2×C4×C73C4×D411yescharacteristic
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73C4×D411yescharacteristic
233C2×C4×C73C4×Q811yescharacteristic
234C2×C4×C73C4×Q811yescharacteristic
235C2×C4×C73C4×Q811yescharacteristic
236C2×C4×C73C4×Q811yescharacteristic
237C2×C4×C73#12111yescharacteristic
238C2×C4×C73C22⋊Q811yescharacteristic
239C2×C4×C73C22⋊Q811yescharacteristic
240C2×C4×C73C22⋊Q811yescharacteristic
241C2×C4×C73#12311yescharacteristic
242C2×C4×C73#12311yescharacteristic
243C2×C4×C73#12411yescharacteristic
244C2×C4×C73#12511yescharacteristic
245C2×C4×C73#12511yescharacteristic
246C2×C4×C73#12611yescharacteristic
247C2×C4×C73#12611yescharacteristic
248C2×C4×C73C4⋊Q811yescharacteristic
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—
263#10596831—24no—
264#10596831—42no—
265C22×C73C4×C4⋊C411yescharacteristic
266C22×C73#38511yescharacteristic
267C22×C73#38511yescharacteristic
268C22×C73#38611yescharacteristic
269C22×C73#38711yescharacteristic
270C22×C73#38811yescharacteristic
271C22×C73#38911yescharacteristic
272C22×C73C2×#10611yescharacteristic
273C22×C73#42711yescharacteristic
274C22×C73#42811yescharacteristic
275C22×C73#42811yescharacteristic
276C22×C73C4×SD1611yescharacteristic
277C22×C73C4×SD1611yescharacteristic
278C22×C73C4×SD1611yescharacteristic
279C22×C73C4×SD1611yescharacteristic
280C22×C73#44011yescharacteristic
281C22×C73#44011yescharacteristic
282C22×C73#44111yescharacteristic
283C22×C73#44211yescharacteristic
284C22×C73#44811yescharacteristic
285C22×C73#44911yescharacteristic
286C22×C73#45011yescharacteristic
287C22×C73#45211yescharacteristic
288C22×C73#46011yescharacteristic
289C22×C73#46111yescharacteristic
290C22×C73#46311yescharacteristic
291C22×C73#46411yescharacteristic
292C22×C73#47511yescharacteristic
293C22×C73#47611yescharacteristic
294C22×C73#47811yescharacteristic
295C22×C73#47911yescharacteristic
296C22×C73#48111yescharacteristic
297C22×C73#48211yescharacteristic
298C22×C73#48311yescharacteristic
299C22×C73#48511yescharacteristic
300C4×C73—24no—
301C4×C73—42no—
302C4×C73—44no—
303C4×C73—44no—
304C4×C73C4×C22⋊C411yescharacteristic
305C4×C73C4×C4⋊C411yescharacteristic
306C4×C73#38711yescharacteristic
307C4×C73#38711yescharacteristic
308C4×C73#38711yescharacteristic
309C4×C73#38811yescharacteristic
310C4×C73#38911yescharacteristic
311C4×C73#39111yescharacteristic
312Dic73—82no—
313Dic73—82no—
314#10908—731nomaximal, Sylow
315C2×C73#143611yescharacteristic
316C2×C73C4×#10611yescharacteristic
317C2×C73#177611yescharacteristic
318C2×C73#185311yescharacteristic
319C2×C73#185411yescharacteristic
320C2×C73#186411yescharacteristic
321C2×C73#186511yescharacteristic
322C2×C73#187711yescharacteristic
323C2×C73#188011yescharacteristic
324C2×C73#191911yescharacteristic
325C2×C73#192011yescharacteristic
326C2×C73#192611yescharacteristic
327C2×C73#192711yescharacteristic
328C2×C73#194811yescharacteristic
329C2×C73#194911yescharacteristic
330C22×#106—731no—
331C2×C4×C4⋊C4D7311yescharacteristic
332C2×#340—731no—
333C2×#340—731no—
334C2×#340—731no—
335C2×#336—731no—
336C4⋊#95—731no—
337C73#1090811yescharacteristic, complemented, Sylow
338C23×C8—731no—
339C23×C8—731no—
340C22×C4⋊C4—731no—
341C22×C4⋊C4—731no—
342C22×C4⋊C4C2×D7311yescharacteristic
343C22×C4⋊C4C2×D7311yescharacteristic
344C22×C42—21no—
345C22×C42C2×D7311yescharacteristic
346C2×#106—734no—
347C2×#106—1462no—
348C2×#106—1462no—
349C4×C4⋊C4—22no—
350C4×C4⋊C4—22no—
351C2×#95—21no—
352C2×#95—1461no—
353C2×#95—1461no—
354#340—734no—
355#340—1462no—
356#340—1462no—
357#336—734no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—1461no—
361C23×C4—1461no—
362C23×C4C22⋊D7311yescharacteristic
363C23×C4C22⋊D7311yescharacteristic
364C23×C4C22×D7311yescharacteristic
365C22×C8—732no—
366C22×C8—732no—
367C22×C8—732no—
368C22×C8—732no—
369C22×C8—1461no—
370C22×C8—1461no—
371C22×C8—1461no—
372C22×C8—1461no—
373C22×C8—1461no—
374C22×C8—1461no—
375C22×C8—1461no—
376C22×C8—1461no—
377C22×C8—1461no—
378C22×C8—1461no—
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—732no—
386C2×C4⋊C4—732no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4—1461no—
389C2×C4⋊C4—1461no—
390C2×C4⋊C4—1461no—
391C2×C4⋊C4—1461no—
392C2×C4⋊C4—1461no—
393C2×C4⋊C4—1461no—
394C2×C4⋊C4—1461no—
395C2×C4⋊C4—1461no—
396C2×C4⋊C4—1461no—
397C2×C4⋊C4Dic14612yes—
398C2×C4⋊C4C4×D7312yes—
399C2×C4⋊C4C4×D7312yes—
400C2×C4⋊C4D29212yes—
401C2×C4⋊C4C22⋊D7312yes—
402C2×C4⋊C4C22⋊D7312yes—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42Dic14612yes—
411C2×C42C4×D7312yes—
412#106—1468no—
413#95—24no—
414#95—2922no—
415#95—2922no—
416C24C2×C22⋊D7311yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—2921no—
442C22×C4—2921no—
443C22×C4—2921no—
444C22×C4—2921no—
445C22×C4—2921no—
446C22×C4—2921no—
447C22×C4—2921no—
448C22×C4—2921no—
449C22×C4—2921no—
450C22×C4—2921no—
451C22×C4—2921no—
452C22×C4—2921no—
453C22×C4—1462no—
454C22×C4—1462no—
455C22×C4#1192400712yes—
456C22×C4#1192400712yes—
457C22×C4#1192401512yes—
458C22×C4#1192401612yes—
459C22×C4C2×C4×D7311yescharacteristic
460C22×C4C2×C4×D7311yescharacteristic
461C22×C4C2×C4×D7311yescharacteristic
462C22×C4C2×C22⋊D7311yescharacteristic
463C22×C4C2×C22⋊D7311yescharacteristic
464C22×C4C2×D29211yescharacteristic
465C22×C4C2×Dic14611yescharacteristic
466C22×C4C2×Dic14611yescharacteristic
467C22×C4#1192402811yescharacteristic
468C22×C4#1192402811yescharacteristic
469C22×C4#1192402811yescharacteristic
470C22×C4#1192402811yescharacteristic
471C22×C4#1192402811yescharacteristic
472C22×C4#1192402811yescharacteristic
473C2×C8—2921no—
474C2×C8—2921no—
475C2×C8—2921no—
476C2×C8—2921no—
477C2×C8—734no—
478C2×C8—1462no—
479C2×C8—1462no—
480C2×C8—1462no—
481C2×C8—1462no—
482C2×C8—1462no—
483C2×C8—1462no—
484C2×C8—1462no—
485C2×C8—1462no—
486C2×C8—1462no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—2921no—
494C4⋊C4—2921no—
495C4⋊C4—2921no—
496C4⋊C4—2921no—
497C4⋊C4—1462no—
498C4⋊C4—1462no—
499C4⋊C4—1462no—
500C4⋊C4—1462no—
501C4⋊C4#1192400514yes—
502C4⋊C4#1192400714yes—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—48no—
508C23C2×#1192400711yescharacteristic
509C23C4×C22⋊D7311yescharacteristic
510C23C4×C22⋊D7311yescharacteristic
511C23#1455656011yescharacteristic
512C23#1455656511yescharacteristic
513C23#1455657011yescharacteristic
514C23#1455657411yescharacteristic
515C23C2×#1192401511yescharacteristic
516C23C2×#1192401611yescharacteristic
517C23#1455661111yescharacteristic
518C23#1455661111yescharacteristic
519C23#1455661611yescharacteristic
520C23#1455661711yescharacteristic
521C23#1455662111yescharacteristic
522C23#1455662211yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—2922no—
551C2×C4—2922no—
552C2×C4—2922no—
553C2×C4—2922no—
554C2×C4—2922no—
555C2×C4—2922no—
556C2×C4—5841no—
557C2×C4—5841no—
558C2×C4—5841no—
559C2×C4—5841no—
560C2×C4—5841no—
561C2×C4—5841no—
562C2×C4—5841no—
563C2×C4—5841no—
564C2×C4#1455652214yescomplemented
565C2×C4C42×D7311yescharacteristic
566C2×C4C2×#1192400511yescharacteristic
567C2×C4C2×#1192400711yescharacteristic
568C2×C4#1455654811yescharacteristic
569C2×C4#1455654811yescharacteristic
570C2×C4#1455654811yescharacteristic
571C2×C4C4×C22⋊D7311yescharacteristic
572C2×C4C4×C22⋊D7311yescharacteristic
573C2×C4C4×C22⋊D7311yescharacteristic
574C2×C4C4×C22⋊D7311yescharacteristic
575C2×C4C4×D29211yescharacteristic
576C2×C4C4×D29211yescharacteristic
577C2×C4C4×Dic14611yescharacteristic
578C2×C4C4×Dic14611yescharacteristic
579C2×C4C4×Dic14611yescharacteristic
580C2×C4C4×Dic14611yescharacteristic
581C2×C4#1455656511yescharacteristic
582C2×C4#1455657011yescharacteristic
583C2×C4#1455657011yescharacteristic
584C2×C4#1455657011yescharacteristic
585C2×C4#1455657411yescharacteristic
586C2×C4#1455657411yescharacteristic
587C2×C4#1455657911yescharacteristic
588C2×C4#1455658311yescharacteristic
589C2×C4#1455658311yescharacteristic
590C2×C4#1455658511yescharacteristic
591C2×C4#1455658511yescharacteristic
592C2×C4#1455659111yescharacteristic
593C8—2922no—
594C8—1464no—
595C22C4×#1192400711yescharacteristic
596C22#1798846011yescharacteristic
597C22#1798846011yescharacteristic
598C22#1798846611yescharacteristic
599C22#1798847111yescharacteristic
600C22#1798847811yescharacteristic
601C22#1798848511yescharacteristic
602C22C2×#1455652211yescharacteristic
603C22#1798862311yescharacteristic
604C22#1798862711yescharacteristic
605C22#1798863011yescharacteristic
606C22C4×#1192401611yescharacteristic
607C22C4×#1192401611yescharacteristic
608C22C4×#1192401511yescharacteristic
609C22C4×#1192401511yescharacteristic
610C22#1798868511yescharacteristic
611C22#1798868711yescharacteristic
612C22#1798869211yescharacteristic
613C22#1798869711yescharacteristic
614C22#1798872611yescharacteristic
615C22#1798873211yescharacteristic
616C22#1798873811yescharacteristic
617C22#1798874911yescharacteristic
618C22#1798878711yescharacteristic
619C22#1798879211yescharacteristic
620C22#1798880211yescharacteristic
621C22#1798880911yescharacteristic
622C22#1798887211yescharacteristic
623C22#1798887711yescharacteristic
624C22#1798888711yescharacteristic
625C22#1798889411yescharacteristic
626C22#1798890511yescharacteristic
627C22#1798891111yescharacteristic
628C22#1798891711yescharacteristic
629C22#1798892811yescharacteristic
630C4—24no—
631C4—44no—
632C4—44no—
633C4—42no—
634C4—5842no—
635C4—5842no—
636C4C4×#1192400511yescharacteristic
637C4C4×#1192400711yescharacteristic
638C4#1798847111yescharacteristic
639C4#1798847111yescharacteristic
640C4#1798847111yescharacteristic
641C4#1798847811yescharacteristic
642C4#1798848511yescharacteristic
643C4#1798849311yescharacteristic
644C2#2260816411yescharacteristic
645C2C4×#1455652211yescharacteristic
646C2#2260982911yescharacteristic
647C2#2261012411yescharacteristic
648C2#2261013011yescharacteristic
649C2#2261019211yescharacteristic
650C2#2261019911yescharacteristic
651C2#2261026511yescharacteristic
652C2#2261028611yescharacteristic
653C2#2261050911yescharacteristic
654C2#2261051611yescharacteristic
655C2#2261055811yescharacteristic
656C2#2261056511yescharacteristic
657C2#2261069411yescharacteristic
658C2#2261069911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D73
commutatorC2×C4×C73C2×C42
FrattiniC23×C4C22×D73
FittingC2×C4×C4⋊C4×C73C2
socle, prime radicalC24×C73C2×D4
cosocleC23×C4×C73C23
hypercenterC2×C4×C4⋊C4D73
hypocenterC73#10908
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C2×#14556522C4semidirect
19. #17988349C4semidirect
20. #17988342C4semidirect
113. C2×#10596831C42semidirect
220. C2×C4×C73#106semidirect
337. C73#10908semidirect
564. C2×C4#14556522semidirect

Maximal subgroups

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

subgroupindex
C22×#145565222
C2×#179883492
C2×#179883422
#226081612
C2×C4×C4⋊C4×C732
#1090873