Finite Group Databasebeta

← #33103243

Subgroups — #33103243

Order 18688.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612824C211yesmaximal, characteristic, complemented
2D4×C22⋊Dic73C211yesmaximal, characteristic
3#22610630C211yesmaximal, characteristic, complemented
4#22610616C211yesmaximal, characteristic, complemented
5#22610560C211yesmaximal, characteristic, complemented
6#22610553C211yesmaximal, characteristic, complemented
7#22610194C211yesmaximal, characteristic, complemented
8#22610180C211yesmaximal, characteristic, complemented
9#22610026C211yesmaximal, characteristic, complemented
10#22609964C211yesmaximal, characteristic, complemented
11#22609862C211yesmaximal, characteristic
12#22609758C211yesmaximal, characteristic, complemented
13#102×Dic73C211yesmaximal, characteristic, complemented
14#22609712C211yesmaximal, characteristic, complemented
15C2×#418×C73C211yesmaximal, characteristic
16C2×D4×Dic73C2211yescharacteristic
17C2×D4×Dic73C2211yescharacteristic
18C22×C22⋊Dic73—21no—
19C2×#14556525C2211yescharacteristic, complemented
20C2×#14556523C2211yescharacteristic, complemented
21C2×#14556512C2211yescharacteristic
22C2×#14556512C2211yescharacteristic
23C2×#14556512C2211yescharacteristic
24C2×#14556512C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×#14556501C2211yescharacteristic, complemented
27C2×C8×Dic73C2211yescharacteristic, complemented
28#17988490C2211yescharacteristic
29#17988490C2211yescharacteristic
30#17988486C2211yescharacteristic, complemented
31#17988486C2211yescharacteristic, complemented
32#17988480—21no—
33#17988480—21no—
34#17988467—21no—
35#17988467—21no—
36#17988455—21no—
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988443—21no—
40C4⋊C4×Dic73C2211yescharacteristic, complemented
41C4⋊C4×Dic73C2211yescharacteristic, complemented
42C4×C4⋊Dic73—21no—
43C4×C22⋊Dic73C2211yescharacteristic
44#17988350C2211yescharacteristic, complemented
45#17988350C2211yescharacteristic, complemented
46#17988349C2211yescharacteristic, complemented
47#17988349C2211yescharacteristic, complemented
48#17988349C2211yescharacteristic, complemented
49#17988349C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52C23×D4×C73C2211yescharacteristic
53C22×M16×C73C2211yescharacteristic
54C2×#117×C73C2211yescharacteristic
55#418×C73C418yescomplemented
56C2×#102×C73C2211yescharacteristic
57C2×#102×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×#102×C73C2211yescharacteristic
60C23×Dic73—21no—
61C23×Dic73—21no—
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64D4×Dic73—22no—
65D4×Dic73—22no—
66D4×Dic73—41no—
67D4×Dic73—41no—
68C2×C4⋊Dic73—21no—
69C2×C4⋊Dic73—21no—
70C2×C4⋊Dic73C2311yescharacteristic
71C2×C4⋊Dic73C2311yescharacteristic
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C22⋊Dic73—21no—
75C2×C22⋊Dic73—21no—
76C2×C22⋊Dic73—21no—
77C2×C22⋊Dic73—21no—
78C2×C22⋊Dic73—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—44no—
83C2×C22⋊Dic73D411yescharacteristic
84C2×C22⋊Dic73D411yescharacteristic
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89#14556525—41no—
90#14556523—41no—
91#14556512—22no—
92#14556512—22no—
93#14556512—41no—
94#14556512—41no—
95C22⋊#10596831—22no—
96#14556501—41no—
97C8×Dic73—41no—
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498D411yescharacteristic
105#14556498D411yescharacteristic
106C25×C73—21no—
107C22×D4×C73—22no—
108C22×D4×C73—22no—
109C22×D4×C73—21no—
110C22×D4×C73—22no—
111C22×D4×C73—41no—
112C22×D4×C73—41no—
113C22×D4×C73C2×C414yes—
114C22×D4×C73C2311yescharacteristic
115C22×D4×C73C2311yescharacteristic
116C23×C4×C73C2311yescharacteristic
117C2×M16×C73—41no—
118C2×M16×C73—41no—
119C2×M16×C73C2×C414yescomplemented
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122#117×C73—22no—
123#117×C73C2×C414yescomplemented
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C22⋊C4×C73—21no—
127C2×C42×C73—21no—
128#102×C73C2×C414yes—
129#102×C73C2×C414yes—
130#102×C73C2×C414yescomplemented
131#102×C73C2×C414yescomplemented
132C22×Dic73—21no—
133C22×Dic73—21no—
134C22×Dic73—21no—
135C22×Dic73—21no—
136C22×Dic73—42no—
137C22×Dic73—42no—
138C22×Dic73—42no—
139C22×Dic73—42no—
140C22×Dic73—81no—
141C22×Dic73—81no—
142C22×Dic73C2×D411yescharacteristic
143C22×Dic73C2×D411yescharacteristic
144C22×Dic73C2×D411yescharacteristic
145C22×Dic73C2×D411yescharacteristic
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—42no—
161C4⋊Dic73—42no—
162C22⋊Dic73—22no—
163C22⋊Dic73—41no—
164C22⋊Dic73—42no—
165C22⋊Dic73—42no—
166C22⋊Dic73—42no—
167C22⋊Dic73—42no—
168C22⋊Dic73—42no—
169C22⋊Dic73—81no—
170C22⋊Dic73—81no—
171C22⋊Dic73—81no—
172C4×Dic73—21no—
173C4×Dic73—21no—
174C4×Dic73—21no—
175C4×Dic73—21no—
176C4×Dic73—81no—
177C4×Dic73—81no—
178C24×C73—21no—
179C24×C73—21no—
180C24×C73—24no—
181C24×C73—42no—
182C24×C73—42no—
183C24×C73—42no—
184C24×C73—42no—
185C24×C73—81no—
186C24×C73—81no—
187C24×C73C2×D411yescharacteristic
188C2×D4×C73—28no—
189C2×D4×C73—24no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—44no—
199C2×D4×C73—44no—
200C2×D4×C73—44no—
201C2×D4×C73—42no—
202C2×D4×C73—42no—
203C2×D4×C73C22×C412yes—
204C2×D4×C73C22×C412yes—
205C2×D4×C73#4112yes—
206C2×D4×C73#4112yes—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73C22×C412yes—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73#4112yes—
216C22×C4×C73C2411yescharacteristic
217M16×C73—44no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73C22×C412yes—
223C2×C8×C73C22×C412yes—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73C22×C412yes—
227C4⋊C4×C73C22×C412yes—
228C22⋊C4×C73—24no—
229C42×C73—24no—
230C23×C73—22no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—22no—
234C23×C73—22no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—22no—
240C23×C73—48no—
241C23×C73—48no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—84no—
253C23×C73—84no—
254C23×C73—84no—
255C23×C73—84no—
256C23×C73—84no—
257C23×C73C4×D412yes—
258C23×C73C22×D411yescharacteristic
259D4×C73—22no—
260D4×C73—22no—
261D4×C73—22no—
262D4×C73—22no—
263D4×C73—22no—
264D4×C73—48no—
265D4×C73—41no—
266D4×C73—41no—
267D4×C73#11714yes—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73C4×D412yes—
281C2×C4×C73C23×C411yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73—41no—
299C2×Dic73—41no—
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—84no—
311C2×Dic73—84no—
312C2×Dic73AGL(1,ℤ/8)12yes—
313C8×C73—22no—
314C8×C73—22no—
315#10596831—41no—
316#10596831—41no—
317C22×C73—22no—
318C22×C73—24no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—42no—
322C22×C73—42no—
323C22×C73—41no—
324C22×C73—42no—
325C22×C73—42no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—41no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—42no—
334C22×C73—816no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73C2×C4×D411yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73#54611yescharacteristic
342C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C73#57511yescharacteristic
344C22×C73#57611yescharacteristic
345C22×C73#57711yescharacteristic
346C4×C73—22no—
347C4×C73—42no—
348C4×C73—42no—
349C4×C73C2×#11711yescharacteristic
350C4×C73#51811yescharacteristic
351C4×C73#55111yescharacteristic
352C4×C73#55111yescharacteristic
353Dic73—22no—
354Dic73—41no—
355Dic73—41no—
356Dic73—41no—
357Dic73—81no—
358Dic73—81no—
359Dic73—81no—
360Dic73—81no—
361#22580—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73—44no—
364C2×C73—82no—
365C2×C73#234211yescharacteristic
366C2×C73C4×AGL(1,ℤ/8)11yescharacteristic
367C2×C73#294611yescharacteristic
368C2×C73#331111yescharacteristic
369C2×C73#331811yescharacteristic
370C2×C73#332211yescharacteristic
371C2×C73#332411yescharacteristic
372C2×#418D7311yescharacteristic
373#2347—731no—
374D4×C22⋊C4—731no—
375#1936—731no—
376#1934—731no—
377#1926—731no—
378#1925—731no—
379#1864—731no—
380#1862—731no—
381#1825—731no—
382#1809—731no—
383#1786—731no—
384#1762—731no—
385C4×#102—731no—
386#1753—731no—
387C73#2258011yescharacteristic, complemented, Sylow
388C23×D4C2×D7311yescharacteristic
389C22×M16C2×D7311yescharacteristic
390C2×C4×D4—731no—
391C2×C4×D4—731no—
392C2×#117C2×D7311yescharacteristic
393C22×C22⋊C4—1461no—
394C2×#107—731no—
395C2×#106—731no—
396#418Dic7318yescomplemented
397C2×#102—731no—
398C2×#102—731no—
399C2×#102—731no—
400C2×#102—731no—
401C2×#102C2×D7311yescharacteristic
402C2×#102C2×D7311yescharacteristic
403C2×#102C2×D7311yescharacteristic
404C2×#102C2×D7311yescharacteristic
405C2×C22⋊C8—731no—
406C2×#97—731no—
407C2×C4×C8—731no—
408#390—731no—
409#390—731no—
410#389—731no—
411#389—731no—
412#388—1461no—
413#388—1461no—
414#386—1461no—
415#386—1461no—
416#383—1461no—
417#380—731no—
418#380—731no—
419#379—1461no—
420C4×C4⋊C4—731no—
421C4×C4⋊C4—731no—
422C4×C4⋊C4—1461no—
423C4×C22⋊C4—731no—
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#336—731no—
431#336—731no—
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C2×Dic7314yes—
440C22×D4C22×D7311yescharacteristic
441C22×D4C22×D7311yescharacteristic
442C23×C4—1461no—
443C23×C4—1461no—
444C23×C4C22×D7311yescharacteristic
445C2×M16—41no—
446C2×M16—41no—
447C2×M16C2×Dic7314yescomplemented
448C22×C8—731no—
449C22×C8—731no—
450C22×C8C22×D7311yescharacteristic
451C22×C8C22×D7311yescharacteristic
452C4×D4—2921no—
453C4×D4—2921no—
454C4×D4—1462no—
455C4×D4—1462no—
456#117—22no—
457#117C2×Dic7314yescomplemented
458C2×C4⋊C4—731no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—1461no—
463C2×C4⋊C4—1461no—
464C2×C4⋊C4C22×D7311yescharacteristic
465C2×C4⋊C4C22×D7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—2924no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C22⋊C4—1461no—
471C2×C22⋊C4—1461no—
472C2×C22⋊C4—1461no—
473C2×C22⋊C4—1461no—
474C2×C22⋊C4—1461no—
475C2×C22⋊C4—1461no—
476C2×C22⋊C4—1461no—
477C2×C22⋊C4—1461no—
478C2×C42—21no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42—1461no—
482C2×C42—1461no—
483#107—2921no—
484#106—2921no—
485#102—2921no—
486#102—2921no—
487#102—1462no—
488#102—1462no—
489#102C2×Dic7314yes—
490#102C2×Dic7314yes—
491#102C2×Dic7314yescomplemented
492#102C2×Dic7314yescomplemented
493C22⋊C8—1462no—
494#97—2921no—
495C4×C8—2921no—
496#95—731no—
497#95—731no—
498#95—1461no—
499#95—1461no—
500#95—1461no—
501#95—1461no—
502#95—1461no—
503#95—1461no—
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24D4×D7311yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4C22×Dic7312yes—
530C2×D4C22×Dic7312yes—
531C2×D4#1192402812yes—
532C2×D4#1192402812yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—2922no—
540C22×C4—2922no—
541C22×C4—2922no—
542C22×C4—2922no—
543C22×C4—5841no—
544C22×C4—5841no—
545C22×C4—731no—
546C22×C4—731no—
547C22×C4—731no—
548C22×C4—731no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4C22×Dic7312yes—
554C22×C4D4×D7311yescharacteristic
555C22×C4#1192402712yes—
556C22×C4C23×D7311yescharacteristic
557M16—44no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8C22×Dic7312yes—
569C2×C8C22×Dic7312yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—2922no—
573C4⋊C4—2922no—
574C4⋊C4—1461no—
575C4⋊C4—1461no—
576C4⋊C4—1461no—
577C4⋊C4—1461no—
578C4⋊C4—1461no—
579C4⋊C4—1461no—
580C4⋊C4—1461no—
581C4⋊C4—1461no—
582C4⋊C4C22×Dic7312yes—
583C4⋊C4C22×Dic7312yes—
584C22⋊C4—24no—
585C22⋊C4—2922no—
586C22⋊C4—2922no—
587C22⋊C4—2922no—
588C22⋊C4—2922no—
589C22⋊C4—2922no—
590C22⋊C4—2921no—
591C22⋊C4—5841no—
592C22⋊C4—5841no—
593C22⋊C4—5841no—
594C22⋊C4—1462no—
595C42—24no—
596C42—5841no—
597C42—5841no—
598C42—1461no—
599C42—1461no—
600C42—1461no—
601C42—1461no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—22no—
606C23—22no—
607C23—21no—
608C23—21no—
609C23—22no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23D4×Dic7312yes—
630C23C2×D4×D7311yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1455655014yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—5844no—
665C2×C4—5844no—
666C2×C4—732no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4D4×Dic7312yes—
679C2×C4C23×Dic7311yescharacteristic
680C2×C4C2×#1192402711yescharacteristic
681C2×C4C2×#1192402811yescharacteristic
682C2×C4C2×#1192402811yescharacteristic
683C2×C4#1455663611yescharacteristic
684C2×C4#1455663611yescharacteristic
685C8—22no—
686C8—22no—
687C8—2921no—
688C8—2921no—
689C22—22no—
690C22—24no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×D4×Dic7311yescharacteristic
712C22#1798922711yescharacteristic
713C22#1798922711yescharacteristic
714C22AGL(1,ℤ/8)×D7311yescharacteristic
715C22#1798938311yescharacteristic
716C22#1798939111yescharacteristic
717C22#1798939711yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—2921no—
722C4—2921no—
723C4—2921no—
724C4—5841no—
725C4—5841no—
726C4—5841no—
727C4—5841no—
728C4—1462no—
729C4C2×#1455655011yescharacteristic
730C4#1798906211yescharacteristic
731C4#1798926311yescharacteristic
732C4#1798926311yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2261278011yescharacteristic
737C2AGL(1,ℤ/8)×Dic7311yescharacteristic
738C2#2261876411yescharacteristic
739C2#2262196811yescharacteristic
740C2#2262207311yescharacteristic
741C2#2262212811yescharacteristic
742C2#2262215811yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#418×C73C2
socleC23×C73C22×D4
prime radicalC23×D4×C73C22
cosocleC22×C4×C73C24
hypercenterC2×#418D73
hypocenterC73#22580
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #22612824C2semidirect
3. #22610630C2semidirect
4. #22610616C2semidirect
5. #22610560C2semidirect
6. #22610553C2semidirect
7. #22610194C2semidirect
8. #22610180C2semidirect
9. #22610026C2semidirect
10. #22609964C2semidirect
12. #22609758C2semidirect
13. #102×Dic73C2semidirect
14. #22609712C2semidirect
19. C2×#14556525C22semidirect
20. C2×#14556523C22semidirect
26. C2×#14556501C22semidirect
27. C2×C8×Dic73C22semidirect
30. #17988486C22semidirect
31. #17988486C22semidirect
40. C4⋊C4×Dic73C22semidirect
41. C4⋊C4×Dic73C22semidirect
44. #17988350C22semidirect
45. #17988350C22semidirect
46. #17988349C22semidirect
47. #17988349C22semidirect
48. #17988349C22semidirect
49. #17988349C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
55. #418×C73C4semidirect
119. C2×M16×C73C2×C4semidirect
123. #117×C73C2×C4semidirect
130. #102×C73C2×C4semidirect
131. #102×C73C2×C4semidirect
387. C73#22580semidirect
396. #418Dic73semidirect
447. C2×M16C2×Dic73semidirect
457. #117C2×Dic73semidirect
491. #102C2×Dic73semidirect
492. #102C2×Dic73semidirect

Maximal subgroups

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

subgroupindex
#226128242
D4×C22⋊Dic732
#226106302
#226106162
#226105602
#226105532
#226101942
#226101802
#226100262
#226099642
#226098622
#226097582
#102×Dic732
#226097122
C2×#418×C732
#2258073