Finite Group Databasebeta

← #33106410

Subgroups — #33106410

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988688C211yesmaximal, characteristic, complemented
2C2×#17988596C211yesmaximal, characteristic, complemented
3#22612973C211yesmaximal, characteristic
4Q8×C22⋊Dic73C211yesmaximal, characteristic, complemented
5#22610787C211yesmaximal, characteristic, complemented
6#22610623C211yesmaximal, characteristic, complemented
7#22610574C211yesmaximal, characteristic, complemented
8#22610370C211yesmaximal, characteristic
9#22610288C211yesmaximal, characteristic, complemented
10#22610267C211yesmaximal, characteristic, complemented
11#22610201C211yesmaximal, characteristic, complemented
12#22610132C211yesmaximal, characteristic, complemented
13#103×Dic73C211yesmaximal, characteristic, complemented
14#22609717C211yesmaximal, characteristic, complemented
15C2×#448×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C2×Q8×Dic73C2211yescharacteristic
18C2×Q8×Dic73C2211yescharacteristic
19C2×D4×Dic73C2211yescharacteristic
20C2×#14556550C2211yescharacteristic
21#17988688—24no—
22C2×#14556525C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24#17988596—24no—
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556515C2211yescharacteristic
29C2×#14556512C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33#17988494—21no—
34#17988494—21no—
35#17988494C2211yescharacteristic
36#17988494C2211yescharacteristic
37#17988490—21no—
38#17988490C2211yescharacteristic
39#17988486C2211yescharacteristic
40#17988480—21no—
41#17988467—21no—
42#17988447—21no—
43#17988447C2211yescharacteristic
44C4⋊C4×Dic73C2211yescharacteristic
45C22⋊C4×Dic73—21no—
46C4×C22⋊Dic73—21no—
47C4×C22⋊Dic73C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988350C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54C23×Q8×C73C2211yescharacteristic
55C22×SD16×C73C2211yescharacteristic
56C22×SD16×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58#448×C73C418yescomplemented
59C2×#103×C73C2211yescharacteristic
60C2×#103×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C23×Dic73—21no—
63C2×#11924012—22no—
64C2×#11924012—22no—
65C2×#11924012—41no—
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68Q8×Dic73—22no—
69Q8×Dic73—22no—
70Q8×Dic73—41no—
71Q8×Dic73—41no—
72D4×Dic73—22no—
73D4×Dic73—41no—
74#14556550—22no—
75#14556550—41no—
76C2×C4⋊Dic73—21no—
77C2×C4⋊Dic73—21no—
78C2×C4⋊Dic73—21no—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×C4⋊Dic73C2311yescharacteristic
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C22⋊Dic73—21no—
88C2×C22⋊Dic73D411yescharacteristic
89C2×C22⋊Dic73D411yescharacteristic
90C2×C4×Dic73—21no—
91C2×C4×Dic73—21no—
92C2×C4×Dic73—21no—
93C2×C4×Dic73—21no—
94C2×C4×Dic73C2311yescharacteristic
95C2×C4×Dic73C2311yescharacteristic
96#14556525—22no—
97#14556523—41no—
98#14556515—22no—
99#14556515—22no—
100#14556515—22no—
101#14556515D414yescomplemented
102#14556512—22no—
103#14556512—41no—
104#14556501—22no—
105C8×Dic73—41no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110#14556498—21no—
111#14556498—21no—
112#14556498—21no—
113#14556498D411yescharacteristic
114#14556498D411yescharacteristic
115C22×Q8×C73—21no—
116C22×Q8×C73—22no—
117C22×Q8×C73—22no—
118C22×Q8×C73—22no—
119C22×Q8×C73—41no—
120C22×Q8×C73—41no—
121C22×Q8×C73C2×C414yescomplemented
122C22×Q8×C73C2311yescharacteristic
123C22×Q8×C73C2311yescharacteristic
124C22×D4×C73—21no—
125C22×D4×C73C2311yescharacteristic
126C23×C4×C73—21no—
127C23×C4×C73C2311yescharacteristic
128C2×SD16×C73—22no—
129C2×SD16×C73—22no—
130C2×SD16×C73—41no—
131C2×SD16×C73—41no—
132C2×SD16×C73C2×C414yes—
133C2×SD16×C73C2×C414yes—
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136#121×C73—22no—
137#121×C73C2×C414yes—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#103×C73C2×C414yescomplemented
141#103×C73C2×C414yescomplemented
142C22⋊C8×C73C2×C414yescomplemented
143C22×Dic73—21no—
144C22×Dic73—21no—
145C22×Dic73—21no—
146C22×Dic73—21no—
147C22×Dic73—42no—
148C22×Dic73—42no—
149C22×Dic73—81no—
150C22×Dic73C2×D411yescharacteristic
151C22×Dic73C2×D411yescharacteristic
152C22×Dic73C2×D411yescharacteristic
153C22×Dic73C2×D411yescharacteristic
154#11924012—44no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831C2×D412yes—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—21no—
165C4⋊Dic73—21no—
166C4⋊Dic73—21no—
167C4⋊Dic73—21no—
168C4⋊Dic73—42no—
169C4⋊Dic73—42no—
170C4⋊Dic73—81no—
171C4⋊Dic73C2×D412yes—
172C22⋊Dic73—22no—
173C22⋊Dic73—41no—
174C22⋊Dic73—42no—
175C22⋊Dic73—42no—
176C22⋊Dic73—42no—
177C22⋊Dic73—42no—
178C22⋊Dic73—81no—
179C4×Dic73—21no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—42no—
184C4×Dic73—42no—
185C4×Dic73—42no—
186C4×Dic73—81no—
187C24×C73—21no—
188C24×C73C2×D411yescharacteristic
189C2×Q8×C73—24no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—21no—
194C2×Q8×C73—28no—
195C2×Q8×C73—21no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73—42no—
200C2×Q8×C73—42no—
201C2×Q8×C73—44no—
202C2×Q8×C73—44no—
203C2×Q8×C73—44no—
204C2×Q8×C73C22×C412yes—
205C2×Q8×C73C22×C412yes—
206C2×Q8×C73C2×D412yes—
207C2×Q8×C73#4112yes—
208C2×D4×C73—24no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—21no—
212C2×D4×C73—21no—
213C2×D4×C73—21no—
214C2×D4×C73—81no—
215C2×D4×C73—81no—
216C2×D4×C73C22×C412yes—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—24no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—42no—
226C22×C4×C73—42no—
227C22×C4×C73C22×C412yes—
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73#4112yes—
230C22×C4×C73C2411yescharacteristic
231SD16×C73—28no—
232SD16×C73—44no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73C22×C412yes—
238C2×C8×C73C22×C412yes—
239C4⋊C4×C73—21no—
240C4⋊C4×C73C22×C412yes—
241C22⋊C4×C73—24no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73C4×D412yes—
256C23×C73C22×D411yescharacteristic
257Q8×C73—22no—
258Q8×C73—22no—
259Q8×C73—22no—
260Q8×C73—22no—
261Q8×C73—22no—
262Q8×C73—48no—
263Q8×C73—41no—
264Q8×C73—41no—
265Q8×C73C4×D414yes—
266D4×C73—22no—
267D4×C73—22no—
268D4×C73—41no—
269D4×C73—41no—
270D4×C73—84no—
271C2×C4×C73—22no—
272C2×C4×C73—21no—
273C2×C4×C73—22no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—48no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73C4×D412yes—
288C2×C4×C73C23×C411yescharacteristic
289C2×C4×C73C22×D411yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293C2×C4×C73H(5,𝔽2)11yescharacteristic
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—22no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—41no—
313C2×Dic73—41no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73—84no—
318C2×Dic73#13712yes—
319C8×C73—22no—
320C8×C73—22no—
321#10596831—22no—
322#10596831—41no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73C2×C4×D411yescharacteristic
338C22×C73D4211yescharacteristic
339C22×C73#54611yescharacteristic
340C22×C73C2×#13711yescharacteristic
341C22×C73#57511yescharacteristic
342C22×C73#57711yescharacteristic
343C22×C73#57711yescharacteristic
344C4×C73—22no—
345C4×C73—24no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73C2×C4×D411yescharacteristic
349C4×C73#51811yescharacteristic
350C4×C73#54611yescharacteristic
351C4×C73#55111yescharacteristic
352Dic73—22no—
353Dic73—41no—
354Dic73—42no—
355Dic73—41no—
356Dic73—41no—
357Dic73—81no—
358Dic73—81no—
359Dic73—81no—
360#22865—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73—82no—
363C2×C73#235811yescharacteristic
364C2×C73C4×#13711yescharacteristic
365C2×C73#294911yescharacteristic
366C2×C73#327511yescharacteristic
367C2×C73#327811yescharacteristic
368C2×C73#332011yescharacteristic
369C2×C73#332111yescharacteristic
370C2×#448D7311yescharacteristic
371C2×#440—731no—
372C2×#419—731no—
373#2363—731no—
374Q8×C22⋊C4—731no—
375#1968—731no—
376#1935—731no—
377#1928—731no—
378#1895—731no—
379#1880—731no—
380#1877—731no—
381#1865—731no—
382#1854—731no—
383C4×#103—731no—
384#1753—731no—
385C73#2286511yescharacteristic, complemented, Sylow
386C23×Q8C2×D7311yescharacteristic
387C22×SD16C2×D7311yescharacteristic
388C22×SD16C2×D7311yescharacteristic
389C22×M16—731no—
390C2×#121C2×D7311yescharacteristic
391C2×C4×Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×D4—731no—
394C2×#117—731no—
395#448Dic7318yescomplemented
396#440—1464no—
397C2×#107—731no—
398C2×#106—731no—
399#419—1464no—
400C2×#103—731no—
401C2×#103—731no—
402C2×#103—731no—
403C2×#103—731no—
404C2×#103C2×D7311yescharacteristic
405C2×#103C2×D7311yescharacteristic
406C2×#102—731no—
407C2×#102—731no—
408C2×C22⋊C8C2×D7311yescharacteristic
409C2×#97—731no—
410C2×C4×C8—731no—
411#391—731no—
412#391—731no—
413#391—1461no—
414#391—1461no—
415#390—731no—
416#390—1461no—
417#389—731no—
418#388—1461no—
419#386—1461no—
420#380—731no—
421#380—1461no—
422C4×C4⋊C4—731no—
423C4×C22⋊C4—731no—
424C4×C22⋊C4—1461no—
425C4×C22⋊C4—1461no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#336—731no—
431#336—731no—
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×Dic7314yescomplemented
439C22×Q8C22×D7311yescharacteristic
440C22×Q8C22×D7311yescharacteristic
441C22×D4—21no—
442C22×D4C22×D7311yescharacteristic
443C23×C4—21no—
444C23×C4—1461no—
445C23×C4C22×D7311yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic7314yes—
451C2×SD16C2×Dic7314yes—
452C2×M16—2921no—
453C2×M16—1462no—
454C2×M16—1462no—
455C22×C8—731no—
456C22×C8—731no—
457C22×C8C22×D7311yescharacteristic
458C22×C8C22×D7311yescharacteristic
459#121—22no—
460#121C2×Dic7314yes—
461C4×Q8—2921no—
462C4×Q8—2921no—
463C4×Q8—1462no—
464C4×Q8—1462no—
465C4×D4—2921no—
466C4×D4—1462no—
467#117—2921no—
468#117—1462no—
469C2×C4⋊C4—731no—
470C2×C4⋊C4—731no—
471C2×C4⋊C4—731no—
472C2×C4⋊C4—731no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4—1461no—
475C2×C4⋊C4—1461no—
476C2×C4⋊C4C22×D7311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—731no—
479C2×C22⋊C4—731no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C42—731no—
486C2×C42—731no—
487C2×C42—1461no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42—1461no—
491#107—1462no—
492#106—2921no—
493#103—734no—
494#103—1462no—
495#103—1462no—
496#103—1462no—
497#103C2×Dic7314yescomplemented
498#103C2×Dic7314yescomplemented
499#102—2921no—
500#102—1462no—
501C22⋊C8C2×Dic7314yescomplemented
502#97—1462no—
503C4×C8—2921no—
504#95—731no—
505#95—731no—
506#95—1461no—
507#95—1461no—
508#95—1461no—
509#95—1461no—
510#95—1461no—
511#95—1461no—
512#95—1461no—
513C24—21no—
514C24D4×D7311yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C22×Dic7312yes—
531C2×Q8C22×Dic7312yes—
532C2×Q8D4×D7312yes—
533C2×Q8#1192402712yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C22×Dic7312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—2922no—
554C22×C4—2922no—
555C22×C4—5841no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—731no—
559C22×C4—731no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4C22×Dic7312yes—
565C22×C4D4×D7311yescharacteristic
566C22×C4#1192402712yes—
567C22×C4C23×D7311yescharacteristic
568SD16—28no—
569SD16—44no—
570M16—2924no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—732no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8C22×Dic7312yes—
582C2×C8C22×Dic7312yes—
583C4⋊C4—21no—
584C4⋊C4—2922no—
585C4⋊C4—2922no—
586C4⋊C4—5841no—
587C4⋊C4—732no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C4⋊C4—1461no—
594C4⋊C4—1461no—
595C4⋊C4C22×Dic7312yes—
596C22⋊C4—24no—
597C22⋊C4—2922no—
598C22⋊C4—2922no—
599C22⋊C4—2922no—
600C22⋊C4—2921no—
601C22⋊C4—2922no—
602C22⋊C4—5841no—
603C22⋊C4—1462no—
604C42—2922no—
605C42—2922no—
606C42—2922no—
607C42—5841no—
608C42—1461no—
609C42—1461no—
610C42—1461no—
611C42—1461no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23D4×Dic7312yes—
626C23C2×D4×D7311yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8D4×Dic7314yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—5844no—
669C2×C4—732no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1462no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4—1461no—
681C2×C4—1461no—
682C2×C4D4×Dic7312yes—
683C2×C4C23×Dic7311yescharacteristic
684C2×C4C2×D4×D7311yescharacteristic
685C2×C4C2×#1192402711yescharacteristic
686C2×C4C2×#1192402711yescharacteristic
687C2×C4#1455663611yescharacteristic
688C2×C4#1455663611yescharacteristic
689C8—22no—
690C8—22no—
691C8—2921no—
692C8—1462no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×D4×Dic7311yescharacteristic
708C22#1798921911yescharacteristic
709C22#1798922411yescharacteristic
710C22#137×D7311yescharacteristic
711C22#1798938611yescharacteristic
712C22#1798939311yescharacteristic
713C22#1798939311yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—2922no—
719C4—2921no—
720C4—2921no—
721C4—2921no—
722C4—5841no—
723C4—5841no—
724C4—5841no—
725C4—1462no—
726C4C2×D4×Dic7311yescharacteristic
727C4#1798906211yescharacteristic
728C4#1798922411yescharacteristic
729C4#1798926811yescharacteristic
730C2—42no—
731C2—82no—
732C2#2261291511yescharacteristic
733C2#137×Dic7311yescharacteristic
734C2#2261879111yescharacteristic
735C2#2262156511yescharacteristic
736C2#2262159511yescharacteristic
737C2#2262209511yescharacteristic
738C2#2262211011yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#448×C73C2
socleC23×C73C22×D4
prime radicalC2×#121×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#448D73
hypocenterC73#22865
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#17988688C2semidirect
2. C2×#17988596C2semidirect
4. Q8×C22⋊Dic73C2semidirect
5. #22610787C2semidirect
6. #22610623C2semidirect
7. #22610574C2semidirect
9. #22610288C2semidirect
10. #22610267C2semidirect
11. #22610201C2semidirect
12. #22610132C2semidirect
13. #103×Dic73C2semidirect
14. #22609717C2semidirect
58. #448×C73C4semidirect
101. #14556515D4semidirect
121. C22×Q8×C73C2×C4semidirect
140. #103×C73C2×C4semidirect
141. #103×C73C2×C4semidirect
142. C22⋊C8×C73C2×C4semidirect
385. C73#22865semidirect
395. #448Dic73semidirect
438. C22×Q8C2×Dic73semidirect
497. #103C2×Dic73semidirect
498. #103C2×Dic73semidirect
501. C22⋊C8C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886882
C2×#179885962
#226129732
Q8×C22⋊Dic732
#226107872
#226106232
#226105742
#226103702
#226102882
#226102672
#226102012
#226101322
#103×Dic732
#226097172
C2×#448×C732
#2286573