Finite Group Databasebeta

← #33104043

Subgroups — #33104043

Order 18688.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2C2×#17988615C211yesmaximal, characteristic, complemented
3C2×#17988610C211yesmaximal, characteristic, complemented
4#22612376C211yesmaximal, characteristic
5#22610652C211yesmaximal, characteristic, complemented
6#22610649C211yesmaximal, characteristic, complemented
7#22610114C211yesmaximal, characteristic, complemented
8#22610114C211yesmaximal, characteristic, complemented
9#22610113C211yesmaximal, characteristic, complemented
10#22610108C211yesmaximal, characteristic, complemented
11#22610084C211yesmaximal, characteristic, complemented
12#22609913C211yesmaximal, characteristic, complemented
13#22609909C211yesmaximal, characteristic, complemented
14#22609789C211yesmaximal, characteristic, complemented
15C2×#436×C73C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4×Dic73C2211yescharacteristic
20#17988659—24no—
21#17988615—24no—
22#17988610—24no—
23C2×C4⋊#10596831C2211yescharacteristic
24C2×#14556520C2211yescharacteristic
25C2×#14556520C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30C2×#14556520C2211yescharacteristic
31C2×#14556520C2211yescharacteristic
32C2×#14556520C2211yescharacteristic
33C2×#14556520C2211yescharacteristic
34C2×C22⋊#10596831C2211yescharacteristic
35C2×C22⋊#10596831C2211yescharacteristic
36C2×#14556502C2211yescharacteristic
37#17988480C411yescharacteristic
38#17988480C411yescharacteristic
39#17988473C411yescharacteristic
40#17988473C411yescharacteristic
41#17988467C411yescharacteristic
42#17988467C411yescharacteristic
43#17988462C411yescharacteristic
44#17988462C411yescharacteristic
45C4×C4⋊Dic73C2211yescharacteristic
46C4×C22⋊Dic73C2211yescharacteristic
47C4×C22⋊Dic73C2211yescharacteristic
48#17988433C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C22×M16×C73C2211yescharacteristic
56C22×M16×C73C2211yescharacteristic
57C2×C4×D4×C73C2211yescharacteristic
58#436×C73—24no—
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63C23×Dic73C2×C411yescharacteristic
64C23×Dic73C2×C411yescharacteristic
65C2×#11924012—22no—
66C2×#11924012—22no—
67C2×#11924012—41no—
68C22×#10596831—22no—
69C22×#10596831—22no—
70C22×#10596831—41no—
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556550—22no—
76#14556550—22no—
77C2×C4⋊Dic73C2×C411yescharacteristic
78C2×C4⋊Dic73C2×C411yescharacteristic
79C2×C4⋊Dic73C2×C411yescharacteristic
80C2×C4⋊Dic73C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C4×Dic73—22no—
88C2×C4×Dic73—22no—
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94C2×C4×Dic73C2311yescharacteristic
95C4⋊#10596831—22no—
96#14556520—22no—
97#14556520—22no—
98#14556520—22no—
99#14556520—22no—
100#14556520—22no—
101#14556520—22no—
102#14556520—22no—
103#14556520—41no—
104#14556520—41no—
105#14556520D414yescomplemented
106C22⋊#10596831—22no—
107C22⋊#10596831—22no—
108#14556502—22no—
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×D4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C2×M16×C73—22no—
123C2×M16×C73—22no—
124C2×M16×C73—22no—
125C2×M16×C73—22no—
126C2×M16×C73—41no—
127C2×M16×C73—41no—
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C22×C8×C73C2311yescharacteristic
131C22×C8×C73C2311yescharacteristic
132C4×D4×C73D414yes—
133C4×D4×C73Q814yes—
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C22⋊C4×C73C2×C411yescharacteristic
136C2×C22⋊C4×C73C2×C411yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—22no—
139C22⋊C8×C73—22no—
140C22⋊C8×C73—22no—
141C4×C8×C73—22no—
142C22×Dic73—22no—
143C22×Dic73—22no—
144C22×Dic73—22no—
145C22×Dic73—41no—
146C22×Dic73—41no—
147C22×Dic73—41no—
148C22×Dic73C22×C411yescharacteristic
149C22×Dic73C22×C411yescharacteristic
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156#11924012—44no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—44no—
169C2×#10596831C2×D412yes—
170C4⋊Dic73—22no—
171C4⋊Dic73—22no—
172C4⋊Dic73—22no—
173C4⋊Dic73—41no—
174C22⋊Dic73—22no—
175C22⋊Dic73—22no—
176C22⋊Dic73—22no—
177C22⋊Dic73—41no—
178C22⋊Dic73—41no—
179C22⋊Dic73—41no—
180C4×Dic73—21no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—22no—
187C4×Dic73—22no—
188C4×Dic73C2×D412yes—
189C4×Dic73#4112yes—
190C24×C73C22×C411yescharacteristic
191C24×C73C22×C411yescharacteristic
192C2×D4×C73—41no—
193C2×D4×C73—41no—
194C2×D4×C73C4⋊C414yes—
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×C73C22×C411yescharacteristic
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C2×D412yes—
208C22×C4×C73C2×D412yes—
209C22×C4×C73C2×Q812yes—
210C22×C4×C73C2×Q812yes—
211C22×C4×C73C2411yescharacteristic
212M16×C73—44no—
213M16×C73—44no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73C2×D412yes—
226C4⋊C4×C73C4⋊C414yes—
227C22⋊C4×C73C4⋊C414yes—
228C22⋊C4×C73C4⋊C414yes—
229C42×C73C2×D412yes—
230C42×C73C2×Q812yes—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73C2×C4⋊C412yes—
244C23×C73C2×C4⋊C412yes—
245C23×C73C23×C411yescharacteristic
246D4×C73—44no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73C2×C4⋊C412yes—
264C2×C4×C73C2×C4⋊C412yes—
265C2×C4×C73C2×C4⋊C412yes—
266C2×C4×C73C2×C4⋊C412yes—
267C2×C4×C73C22×D411yescharacteristic
268C2×C4×C73C22×D411yescharacteristic
269C2×C4×C73C22×Q811yescharacteristic
270C2×C4×C73C2×#4111yescharacteristic
271C2×C4×C73H(5,𝔽2)11yescharacteristic
272C2×C4×C732−1+411yescharacteristic
273C2×Dic73—21no—
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—44no—
295C2×Dic73—44no—
296C2×Dic73C4×D412yes—
297C2×Dic73C4×D412yes—
298C2×Dic73#13112yes—
299C8×C73—22no—
300C8×C73—41no—
301C8×C73—41no—
302C8×C73—41no—
303#10596831—22no—
304#10596831—41no—
305#10596831—41no—
306#10596831—41no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73C22×C4⋊C411yescharacteristic
322C22×C73C2×C4×D411yescharacteristic
323C22×C73#52011yescharacteristic
324C22×C73C2×#13111yescharacteristic
325C22×C73#56811yescharacteristic
326C22×C73#56811yescharacteristic
327C22×C73#56811yescharacteristic
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—22no—
331C4×C73—22no—
332C4×C73D4211yescharacteristic
333C4×C73#54711yescharacteristic
334C4×C73D4×Q811yescharacteristic
335C4×C73#55411yescharacteristic
336Dic73—22no—
337Dic73—22no—
338Dic73—22no—
339Dic73—41no—
340Dic73—41no—
341Dic73—41no—
342Dic73—41no—
343Dic73—41no—
344#22649—731nomaximal, Sylow
345C2×C73—42no—
346C2×C73—42no—
347C2×C73D4×C4⋊C411yescharacteristic
348C2×C73#290511yescharacteristic
349C2×C73#290611yescharacteristic
350C2×C73#293011yescharacteristic
351C2×C73#293311yescharacteristic
352C2×C73#299311yescharacteristic
353C2×C73#299511yescharacteristic
354C2×#436D7311yescharacteristic
355C2×#435—731no—
356C2×#424—731no—
357C2×#423—731no—
358#2290—731no—
359#1940—731no—
360#1939—731no—
361#1851—731no—
362#1851—731no—
363#1851—731no—
364#1850—731no—
365#1843—731no—
366#1798—731no—
367#1797—731no—
368#1768—731no—
369C73#2264911yescharacteristic, complemented, Sylow
370C22×M16—731no—
371C22×M16C2×D7311yescharacteristic
372C22×M16C2×D7311yescharacteristic
373C23×C8—731no—
374C2×C4×D4C2×D7311yescharacteristic
375C2×#117—731no—
376C22×C42—731no—
377#436—24no—
378#435—1464no—
379#424—1464no—
380#423—1464no—
381C2×C4⋊C8—731no—
382C2×C4⋊C8—731no—
383C2×C4⋊C8—731no—
384C2×C4⋊C8—731no—
385C2×C4⋊C8—731no—
386C2×C4⋊C8—731no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8—731no—
391C2×C4⋊C8—731no—
392C2×C4⋊C8C2×D7311yescharacteristic
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8C2×D7311yescharacteristic
396C2×C22⋊C8C2×D7311yescharacteristic
397C2×#97—731no—
398C2×C4×C8C2×D7311yescharacteristic
399#388—731no—
400#388—731no—
401#387—731no—
402#387—731no—
403#386—731no—
404#386—731no—
405#385—731no—
406#385—731no—
407C4×C4⋊C4—731no—
408C4×C22⋊C4—731no—
409C4×C22⋊C4—731no—
410#376—731no—
411#336—731no—
412#336—731no—
413#336—731no—
414#336—731no—
415#336—731no—
416#336—731no—
417C22×D4C4×D7311yescharacteristic
418C23×C4—731no—
419C23×C4—731no—
420C23×C4C22×D7311yescharacteristic
421C23×C4C22×D7311yescharacteristic
422C2×M16—22no—
423C2×M16—22no—
424C2×M16—22no—
425C2×M16—22no—
426C2×M16—41no—
427C2×M16—41no—
428C2×M16—2921no—
429C2×M16—1462no—
430C2×M16—1462no—
431C22×C8—2921no—
432C22×C8—731no—
433C22×C8—731no—
434C22×C8—731no—
435C22×C8—731no—
436C22×C8—1462no—
437C22×C8—1462no—
438C22×C8C22×D7311yescharacteristic
439C22×C8C22×D7311yescharacteristic
440C22×C8C22×D7311yescharacteristic
441C22×C8C22×D7311yescharacteristic
442C4×D4Dic14614yes—
443C4×D4C22⋊D7314yes—
444#117—1462no—
445#117—1462no—
446C2×C4⋊C4—731no—
447C2×C4⋊C4—731no—
448C2×C4⋊C4—731no—
449C2×C4⋊C4—731no—
450C2×C4⋊C4C4×D7311yescharacteristic
451C2×C22⋊C4—731no—
452C2×C22⋊C4—731no—
453C2×C22⋊C4—731no—
454C2×C22⋊C4—731no—
455C2×C22⋊C4—731no—
456C2×C22⋊C4—731no—
457C2×C22⋊C4C4×D7311yescharacteristic
458C2×C22⋊C4C4×D7311yescharacteristic
459C2×C42—731no—
460C2×C42—731no—
461C2×C42—731no—
462C2×C42—731no—
463C2×C42—731no—
464C2×C42—731no—
465C2×C42—1462no—
466C2×C42—1462no—
467C2×C42C22×D7311yescharacteristic
468C4⋊C8—22no—
469C4⋊C8—2921no—
470C4⋊C8—2921no—
471C4⋊C8—734no—
472C4⋊C8—1462no—
473C4⋊C8—1462no—
474C4⋊C8—1462no—
475C4⋊C8—1462no—
476C4⋊C8—1462no—
477C4⋊C8—1462no—
478C4⋊C8—1462no—
479C4⋊C8—1462no—
480C22⋊C8—22no—
481C22⋊C8—22no—
482C22⋊C8—1462no—
483C22⋊C8—1462no—
484#97—1462no—
485C4×C8—22no—
486#95—731no—
487#95—731no—
488#95—731no—
489#95—731no—
490#95—731no—
491#95—731no—
492#95—731no—
493#95—731no—
494#95—731no—
495#95—731no—
496C24C2×C4×D7311yescharacteristic
497C24C2×C4×D7311yescharacteristic
498C2×D4—41no—
499C2×D4—41no—
500C2×D4#1192400714yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—2921no—
510C22×C4—2921no—
511C22×C4—2921no—
512C22×C4—731no—
513C22×C4—731no—
514C22×C4—731no—
515C22×C4—731no—
516C22×C4—731no—
517C22×C4—731no—
518C22×C4—731no—
519C22×C4—731no—
520C22×C4—1462no—
521C22×C4—1462no—
522C22×C4—1462no—
523C22×C4C2×C4×D7311yescharacteristic
524C22×C4C2×C4×D7311yescharacteristic
525C22×C4C2×C4×D7311yescharacteristic
526C22×C4C2×C4×D7311yescharacteristic
527C22×C4C2×C22⋊D7312yes—
528C22×C4C2×C22⋊D7312yes—
529C22×C4C2×Dic14612yes—
530C22×C4C2×Dic14612yes—
531C22×C4C23×D7311yescharacteristic
532M16—44no—
533M16—44no—
534M16—2924no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—2924no—
547C2×C8—732no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8D4×D7312yes—
560C4⋊C4—2921no—
561C4⋊C4—1462no—
562C4⋊C4—1462no—
563C4⋊C4—1462no—
564C4⋊C4#1192400714yes—
565C22⋊C4—2921no—
566C22⋊C4—2921no—
567C22⋊C4—2921no—
568C22⋊C4—1462no—
569C22⋊C4—1462no—
570C22⋊C4—1462no—
571C22⋊C4#1192400714yes—
572C22⋊C4#1192400714yes—
573C42—732no—
574C42—732no—
575C42—1462no—
576C42—1462no—
577C42—1461no—
578C42—1461no—
579C42—1461no—
580C42—1461no—
581C42—1461no—
582C42—1461no—
583C42C2×C22⋊D7312yes—
584C42C2×Dic14612yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C2×#1192400712yes—
598C23C2×#1192400712yes—
599C23C22×C4×D7311yescharacteristic
600D4—44no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—2924no—
618C2×C4—2924no—
619C2×C4—732no—
620C2×C4—732no—
621C2×C4—732no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4—1461no—
627C2×C4—1461no—
628C2×C4—1461no—
629C2×C4—1461no—
630C2×C4—1461no—
631C2×C4—1461no—
632C2×C4—1461no—
633C2×C4—1461no—
634C2×C4—1461no—
635C2×C4—1461no—
636C2×C4—1461no—
637C2×C4—1461no—
638C2×C4—1461no—
639C2×C4—1461no—
640C2×C4—1461no—
641C2×C4—1461no—
642C2×C4—1461no—
643C2×C4C2×#1192400712yes—
644C2×C4C2×#1192400712yes—
645C2×C4C2×#1192400712yes—
646C2×C4C2×#1192400712yes—
647C2×C4C2×D4×D7311yescharacteristic
648C2×C4C22×C22⋊D7311yescharacteristic
649C2×C4C22×Dic14611yescharacteristic
650C2×C4#41×D7311yescharacteristic
651C2×C4#1455663611yescharacteristic
652C2×C4#1455663811yescharacteristic
653C8—22no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—2921no—
658C8—2921no—
659C8—2921no—
660C8—1462no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22C22×#1192400711yescharacteristic
676C22C4×D4×D7311yescharacteristic
677C22#1798906611yescharacteristic
678C22#131×D7311yescharacteristic
679C22#1798935211yescharacteristic
680C22#1798935311yescharacteristic
681C22#1798935311yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—2921no—
687C4—2921no—
688C4—2921no—
689C4—2921no—
690C4—2921no—
691C4—1462no—
692C4—1462no—
693C4—1462no—
694C4D4×C22⋊D7311yescharacteristic
695C4#1798923611yescharacteristic
696C4D4×Dic14611yescharacteristic
697C4#1798929611yescharacteristic
698C2—42no—
699C2—42no—
700C2D4×#1192400711yescharacteristic
701C2#2261849411yescharacteristic
702C2#2261849711yescharacteristic
703C2#2261863111yescharacteristic
704C2#2261866011yescharacteristic
705C2#2261907711yescharacteristic
706C2#2261909511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#436×C73C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenterC2×#436D73
hypocenterC73#22649
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#17988615C2semidirect
3. C2×#17988610C2semidirect
5. #22610652C2semidirect
6. #22610649C2semidirect
7. #22610114C2semidirect
8. #22610114C2semidirect
9. #22610113C2semidirect
10. #22610108C2semidirect
11. #22610084C2semidirect
12. #22609913C2semidirect
13. #22609909C2semidirect
14. #22609789C2semidirect
105. #14556520D4semidirect
369. C73#22649semidirect

Maximal subgroups

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

subgroupindex
C2×#179886592
C2×#179886152
C2×#179886102
#226123762
#226106522
#226106492
#226101142
#226101132
#226101082
#226100842
#226099132
#226099092
#226097892
C2×#436×C732
#2264973