Finite Group Databasebeta

← #33108522

Subgroups — #33108522

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619509C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic, complemented
3#22618658C211yesmaximal, characteristic, complemented
4#22618656C211yesmaximal, characteristic, complemented
5C22×#14556526C211yesmaximal, characteristic, complemented
6#22610816C211yesmaximal, characteristic, complemented
7#22610678C211yesmaximal, characteristic, complemented
8#22610582C211yesmaximal, characteristic, complemented
9#22610577C211yesmaximal, characteristic, complemented
10#22610231C211yesmaximal, characteristic, complemented
11#22610207C211yesmaximal, characteristic, complemented
12#22610204C211yesmaximal, characteristic, complemented
13#22609809C211yesmaximal, characteristic, complemented
14C22⋊C4×#10596831C211yesmaximal, characteristic, complemented
15C73×#1871C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556599C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19C22×#11924012C2211yescharacteristic
20C23×#10596831C2211yescharacteristic
21#17989098C2211yescharacteristic
22#17988826C411yescharacteristic, complemented
23#17988826C411yescharacteristic, complemented
24#17988821C411yescharacteristic, complemented
25#17988821C411yescharacteristic, complemented
26#17988818C411yescharacteristic, complemented
27#17988818C411yescharacteristic, complemented
28#17988814C411yescharacteristic, complemented
29#17988814C411yescharacteristic, complemented
30#17988701—24no—
31#17988665—21no—
32#17988663—21no—
33#17988659—21no—
34#17988659—21no—
35#17988658—21no—
36#17988656—21no—
37D4×#10596831—21no—
38C8×C22⋊D73—21no—
39C2×#14556526—24no—
40C2×#14556526C2211yescharacteristic
41C2×#14556526C2211yescharacteristic
42C2×#14556526C2211yescharacteristic
43C2×#14556526C2211yescharacteristic
44#17988623C2211yescharacteristic
45#17988615C2211yescharacteristic
46#17988614C2211yescharacteristic
47C2×#14556519C2211yescharacteristic
48C2×#14556519C2211yescharacteristic
49#17988583C2211yescharacteristic
50#17988581C2211yescharacteristic
51#17988555C2211yescharacteristic
52#17988554C2211yescharacteristic
53C2×C22⋊#10596831C2211yescharacteristic
54#17988545C2211yescharacteristic
55#17988543C2211yescharacteristic
56C2×C4×#10596831C2211yescharacteristic
57C2×C4×#10596831C2211yescharacteristic
58#17988347C2211yescharacteristic
59#17988347C2211yescharacteristic
60#17988342C2211yescharacteristic
61#17988342C2211yescharacteristic
62C22×M16×C73C2211yescharacteristic
63#525×C73C2211yescharacteristic
64C2×#104×C73C2211yescharacteristic
65C2×#104×C73C2211yescharacteristic
66C4×C22⋊C4×C73C2211yescharacteristic
67#339×C73C2211yescharacteristic
68#339×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70#14556611—22no—
71#14556611—22no—
72C2×#11924018C2×C411yescharacteristic
73C2×#11924016C2×C411yescharacteristic
74C2×#11924015C2×C411yescharacteristic
75C2×#11924013C2×C411yescharacteristic
76#14556599—22no—
77#14556599—41no—
78#14556598—22no—
79#14556598—41no—
80C2×#11924012—21no—
81C2×#11924012—22no—
82C2×#11924012—21no—
83C2×#11924012—41no—
84C2×#11924012C2311yescharacteristic
85C2×#11924012C2311yescharacteristic
86C2×#11924011—21no—
87C22×#10596831—22no—
88C22×#10596831—22no—
89C22×#10596831—21no—
90C22×#10596831—21no—
91C22×#10596831C2×C411yescharacteristic
92C22×#10596831C2×C411yescharacteristic
93C22×#10596831C2×C411yescharacteristic
94C22×#10596831C2×C411yescharacteristic
95C22×#10596831C2311yescharacteristic
96C22×#10596831C2311yescharacteristic
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C2×C8×D73—21no—
100#14556574—21no—
101#14556570C2×C411yescharacteristic
102#14556570C2×C411yescharacteristic
103#14556565C2×C411yescharacteristic
104#14556565C2×C411yescharacteristic
105#14556560—21no—
106C4×C22⋊D73—21no—
107C4×C22⋊D73—21no—
108#14556550C2311yescharacteristic
109#14556526—22no—
110#14556526—22no—
111#14556526—22no—
112#14556526D414yescomplemented
113#14556524C2×C411yescharacteristic
114#14556524C2×C411yescharacteristic
115#14556522C2×C411yescharacteristic
116#14556522C2×C411yescharacteristic
117C4⋊#10596831—21no—
118C4⋊#10596831—21no—
119#14556520—21no—
120#14556520—21no—
121#14556519—22no—
122#14556519—41no—
123#14556515C2×C411yescharacteristic
124#14556515C2×C411yescharacteristic
125#14556514C2×C411yescharacteristic
126#14556514C2×C411yescharacteristic
127#14556512C2×C411yescharacteristic
128#14556512C2×C411yescharacteristic
129#14556511C2×C411yescharacteristic
130#14556511C2×C411yescharacteristic
131C22⋊#10596831—21no—
132C22⋊#10596831—21no—
133C22⋊#10596831D411yescharacteristic
134C22⋊#10596831D411yescharacteristic
135C22⋊#10596831D411yescharacteristic
136C22⋊#10596831D411yescharacteristic
137#14556503—21no—
138#14556503—21no—
139#14556502—21no—
140#14556501—21no—
141C4×#10596831—21no—
142C4×#10596831—22no—
143C4×#10596831—22no—
144C8×Dic73—21no—
145C2×#41×C73C2311yescharacteristic
146C23×C4×C73C2311yescharacteristic
147C2×M16×C73—21no—
148C2×M16×C73—22no—
149C2×M16×C73—41no—
150C2×M16×C73C2311yescharacteristic
151C2×M16×C73C2311yescharacteristic
152C22×C8×C73—21no—
153#123×C73—21no—
154C22⋊Q8×C73C2×C411yescharacteristic
155C22⋊Q8×C73C2×C411yescharacteristic
156#121×C73C2×C411yescharacteristic
157#121×C73C2×C411yescharacteristic
158#120×C73—21no—
159C4×D4×C73—21no—
160C4×D4×C73—21no—
161#117×C73C2311yescharacteristic
162C2×C22⋊C4×C73—21no—
163C2×C42×C73C2311yescharacteristic
164C2×C42×C73C2311yescharacteristic
165#104×C73—22no—
166#104×C73—41no—
167#95×C73—21no—
168#11924028—21no—
169#11924028—21no—
170#11924028—21no—
171#11924028—21no—
172C2×Dic146C22×C411yescharacteristic
173C2×D292C22×C411yescharacteristic
174C2×C22⋊D73—21no—
175C2×C22⋊D73—21no—
176C2×C22⋊D73—21no—
177C2×C4×D73—21no—
178#11924018—22no—
179#11924016—22no—
180#11924015—22no—
181#11924013—22no—
182#11924012—21no—
183#11924012—21no—
184#11924012—21no—
185#11924012—42no—
186#11924012—42no—
187#11924012C2×D412yes—
188#11924011—42no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—22no—
197C2×#10596831—22no—
198C2×#10596831—22no—
199C2×#10596831—22no—
200C2×#10596831—21no—
201C2×#10596831—42no—
202C2×#10596831—42no—
203C2×#10596831C22×C411yescharacteristic
204C2×#10596831C22×C411yescharacteristic
205C2×#10596831C22×C411yescharacteristic
206C2×#10596831C22×C411yescharacteristic
207C2×#10596831C2×D411yescharacteristic
208C2×#10596831C2×D411yescharacteristic
209C2×#10596831C2×D411yescharacteristic
210C2×#10596831C2×D411yescharacteristic
211C2×#10596831C2×D412yes—
212C2×#10596831#4112yes—
213C8×D73—42no—
214C4⋊Dic73C22×C411yescharacteristic
215C4⋊Dic73C22×C411yescharacteristic
216#11924007—21no—
217#11924007—21no—
218C22⋊Dic73—21no—
219C22⋊Dic73—21no—
220C22⋊Dic73—21no—
221#11924005—21no—
222#11924005—21no—
223C4×Dic73—21no—
224C24×C73#4111yescharacteristic
225#41×C73—21no—
226#41×C73—21no—
227#41×C73—21no—
228#41×C73—21no—
229C2×Q8×C73C22×C411yescharacteristic
230C2×D4×C73—21no—
231C2×D4×C73—21no—
232C2×D4×C73—21no—
233C2×D4×C73C22×C411yescharacteristic
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73C22×C411yescharacteristic
242C22×C4×C73C22×C411yescharacteristic
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73#4111yescharacteristic
246C22×C4×C73C2411yescharacteristic
247M16×C73—21no—
248M16×C73—21no—
249M16×C73—21no—
250M16×C73—42no—
251M16×C73C2×D412yes—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—42no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73C22×C411yescharacteristic
258C4⋊C4×C73C22×C411yescharacteristic
259C22⋊C4×C73—24no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—21no—
262C22⋊C4×C73—21no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—21no—
265C42×C73—21no—
266C42×C73—21no—
267C42×C73—21no—
268C42×C73—21no—
269C42×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—22no—
273C23×C73—21no—
274C23×C73—41no—
275C23×C73C4×D411yescharacteristic
276C23×C73C4×D411yescharacteristic
277C23×C73C2×#4111yescharacteristic
278C22×D73—21no—
279Q8×C73—21no—
280Q8×C73—21no—
281D4×C73—21no—
282D4×C73—21no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—42no—
286D4×C73—81no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73C4×D411yescharacteristic
309C2×C4×C73C4×D411yescharacteristic
310C2×C4×C73C23×C411yescharacteristic
311C2×C4×C73C22×D411yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C2×#4111yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C2×C4×C732−1+411yescharacteristic
316C22⋊D73—41no—
317C22⋊D73—41no—
318C22⋊D73—42no—
319C22⋊D73—81no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323D292—21no—
324D292—21no—
325C4×D73—41no—
326C4×D73—41no—
327Dic146—21no—
328Dic146—21no—
329C8×C73—22no—
330C8×C73—41no—
331#10596831—21no—
332#10596831—21no—
333#10596831—21no—
334#10596831—21no—
335#10596831—22no—
336#10596831—21no—
337#10596831—21no—
338#10596831—41no—
339#10596831C4×D412yes—
340#10596831C4×D412yes—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—21no—
346C22×C73—21no—
347C22×C73—21no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73#44312yescomplemented
354C22×C73C2×C4×D411yescharacteristic
355C22×C73#54811yescharacteristic
356C22×C73#55311yescharacteristic
357C2×D73—41no—
358C2×D73—41no—
359C2×D73—41no—
360C4×C73—21no—
361C4×C73—21no—
362C4×C73—42no—
363C4×C73—42no—
364C4×C73—41no—
365C4×C73—41no—
366C4×C73—41no—
367C4×C73C2×C4×D411yescharacteristic
368C4×C73#52011yescharacteristic
369C4×C73D4211yescharacteristic
370C4×C73#54711yescharacteristic
371Dic73—41no—
372Dic73—41no—
373Dic73—41no—
374#23018—731nomaximal, Sylow
375C2×C73—21no—
376C2×C73—21no—
377C2×C73—22no—
378C2×C73—41no—
379C2×C73—81no—
380C2×C73#236111yescharacteristic
381C2×C73C2×#44311yescharacteristic
382C2×C73#295711yescharacteristic
383D73—81no—
384#3050—731no—
385C2×#443—731no—
386#2933—731no—
387#2933—731no—
388C22×#108—731no—
389#1974—731no—
390#1945—731no—
391#1929—731no—
392#1929—731no—
393#1871—731no—
394#1871D7311yescharacteristic, complemented
395#1866—731no—
396#1866—731no—
397#1772—731no—
398C8×C22⋊C4—731no—
399C73#2301811yescharacteristic, complemented, Sylow
400C2×#135—731no—
401C2×#131—731no—
402C2×#131—731no—
403C22×M16—731no—
404C22×M16C2×D7311yescharacteristic
405C23×C8—731no—
406#525—731no—
407#525C2×D7311yescharacteristic
408#467—731no—
409#467—731no—
410#466—731no—
411#466—731no—
412#465—731no—
413#465—731no—
414#465—731no—
415#465—731no—
416#443—1464no—
417#436—1461no—
418#436—1461no—
419#435—1461no—
420#435—1461no—
421#435—1461no—
422#435—1461no—
423C8×D4—1461no—
424C8×D4—1461no—
425C2×#108—731no—
426C2×#108—731no—
427C2×#108—731no—
428C2×#108—731no—
429C2×#108—1464no—
430#427—731no—
431#424—731no—
432#424—731no—
433C2×#104—731no—
434C2×#104—731no—
435C2×#104C2×D7311yescharacteristic
436C2×#104C2×D7311yescharacteristic
437#416—731no—
438#416—731no—
439#408—731no—
440#408—731no—
441C2×C22⋊C8—731no—
442#405—731no—
443#405—731no—
444C2×C4×C8—731no—
445C2×C4×C8—731no—
446C4×C22⋊C4C2×D7311yescharacteristic
447#339—731no—
448#339—731no—
449#339C2×D7311yescharacteristic
450#339C2×D7311yescharacteristic
451#336—731no—
452#336—731no—
453C2×#41—731no—
454C2×#41C22×D7311yescharacteristic
455C23×C4C22×D7311yescharacteristic
456#135—1462no—
457#135—1462no—
458C2×Q16—731no—
459C2×SD16—731no—
460C2×SD16—731no—
461C2×D8—731no—
462#131—2921no—
463#131—2921no—
464#131—1462no—
465#131—1462no—
466C2×M16—21no—
467C2×M16—22no—
468C2×M16—41no—
469C2×M16—2921no—
470C2×M16—731no—
471C2×M16—731no—
472C2×M16—1461no—
473C2×M16—1462no—
474C2×M16—1461no—
475C2×M16—1461no—
476C2×M16C22×D7311yescharacteristic
477C2×M16C22×D7311yescharacteristic
478C22×C8—21no—
479C22×C8—731no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—731no—
487C22×C8—1461no—
488C22×C8—1461no—
489C22×C8—1461no—
490C22×C8—1462no—
491C22×C8—1462no—
492#123—21no—
493#123—1461no—
494C22⋊Q8—731no—
495C22⋊Q8—731no—
496C22⋊Q8C4×D7311yescharacteristic
497C22⋊Q8C4×D7311yescharacteristic
498#121—731no—
499#121—731no—
500#121C4×D7311yescharacteristic
501#121C4×D7311yescharacteristic
502#120—21no—
503#120—1461no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—1461no—
507C4×D4—1461no—
508#117—731no—
509#117C22×D7311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C42C22×D7311yescharacteristic
512C2×C42C22×D7311yescharacteristic
513#108—734no—
514#108—1462no—
515#108—1462no—
516#108—1462no—
517#107—731no—
518#107—731no—
519#106—731no—
520#106—731no—
521C4⋊C8—1461no—
522C4⋊C8—1461no—
523C4⋊C8—1461no—
524C4⋊C8—1461no—
525#104—22no—
526#104—41no—
527#104—2921no—
528#104—1462no—
529#103—731no—
530#103—731no—
531#103—731no—
532#103—731no—
533#102—731no—
534#102—731no—
535#102—731no—
536#102—731no—
537C22⋊C8—731no—
538C22⋊C8—731no—
539C22⋊C8—731no—
540C22⋊C8—731no—
541C22⋊C8—1461no—
542C22⋊C8—1461no—
543C22⋊C8—1461no—
544C22⋊C8—1461no—
545#97—1461no—
546#97—1461no—
547C4×C8—1462no—
548C4×C8—1462no—
549C4×C8—1461no—
550C4×C8—1461no—
551#95—21no—
552C24#1192402711yescharacteristic
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—1461no—
558#41—1461no—
559#41—1461no—
560#41—1461no—
561C2×Q8—731no—
562C2×Q8C2×C4×D7311yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—731no—
567C2×D4—1461no—
568C2×D4—1461no—
569C2×D4—1461no—
570C2×D4C2×C4×D7311yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—1461no—
579C22×C4C2×C4×D7311yescharacteristic
580C22×C4C2×C4×D7311yescharacteristic
581C22×C4D4×D7311yescharacteristic
582C22×C4D4×D7311yescharacteristic
583C22×C4#1192402711yescharacteristic
584C22×C4C23×D7311yescharacteristic
585Q16—1462no—
586SD16—1462no—
587SD16—1462no—
588D8—1462no—
589M16—21no—
590M16—21no—
591M16—21no—
592M16—42no—
593M16—2922no—
594M16—2922no—
595M16—2922no—
596M16—732no—
597M16—1461no—
598M16—1461no—
599M16—1461no—
600M16D4×D7312yes—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—42no—
604C2×C8—2922no—
605C2×C8—2922no—
606C2×C8—2922no—
607C2×C8—731no—
608C2×C8—731no—
609C2×C8—732no—
610C2×C8—732no—
611C2×C8—731no—
612C2×C8—731no—
613C2×C8—731no—
614C2×C8—731no—
615C2×C8—731no—
616C2×C8—731no—
617C2×C8—1461no—
618C2×C8—1462no—
619C2×C8—1462no—
620C2×C8—1462no—
621C2×C8—1462no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—731no—
632C4⋊C4—731no—
633C4⋊C4—1461no—
634C4⋊C4—1461no—
635C4⋊C4C2×C4×D7311yescharacteristic
636C4⋊C4C2×C4×D7311yescharacteristic
637C22⋊C4—24no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—1461no—
644C22⋊C4—1461no—
645C22⋊C4—1461no—
646C22⋊C4—1461no—
647C22⋊C4—1461no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—1461no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—41no—
659C23—1461no—
660C23#1455655111yescharacteristic
661C23#1455655111yescharacteristic
662C23C2×#1192402711yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—1461no—
666Q8—1461no—
667D4—21no—
668D4—21no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—81no—
673D4—2922no—
674D4—2921no—
675D4—2921no—
676D4—5841no—
677D4—1461no—
678D4—1461no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—2921no—
701C2×C4—2921no—
702C2×C4—1461no—
703C2×C4—1461no—
704C2×C4—1461no—
705C2×C4#1455655111yescharacteristic
706C2×C4#1455655111yescharacteristic
707C2×C4C22×C4×D7311yescharacteristic
708C2×C4C2×D4×D7311yescharacteristic
709C2×C4C2×D4×D7311yescharacteristic
710C2×C4#41×D7311yescharacteristic
711C2×C4#1455663611yescharacteristic
712C2×C4#1455663811yescharacteristic
713C8—22no—
714C8—41no—
715C8—2921no—
716C8—732no—
717C8—732no—
718C8—1461no—
719C8—1462no—
720C8—1461no—
721C8—1461no—
722C8—1461no—
723C8—1461no—
724C8—1461no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—2921no—
738C22—2921no—
739C22—2921no—
740C22#1798870112yescomplemented
741C22C2×#1455655111yescharacteristic
742C22#1798924311yescharacteristic
743C22#1798928011yescharacteristic
744C4—21no—
745C4—21no—
746C4—42no—
747C4—42no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—2921no—
752C4—2921no—
753C4—2921no—
754C4C4×D4×D7311yescharacteristic
755C4#1798906611yescharacteristic
756C4#1798921911yescharacteristic
757C4#1798923511yescharacteristic
758C2—21no—
759C2—21no—
760C2—22no—
761C2—41no—
762C2—81no—
763C2—5841no—
764C2#2261294211yescharacteristic
765C2C2×#1798870111yescharacteristic
766C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1871C2
socleC22×C73C2×C4×D4
prime radical#22619509C2
cosocleC22×C4×C73C24
hypercenter#1871D73
hypocenterC73#23018
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618658C2semidirect
4. #22618656C2semidirect
5. C22×#14556526C2semidirect
6. #22610816C2semidirect
7. #22610678C2semidirect
8. #22610582C2semidirect
9. #22610577C2semidirect
10. #22610231C2semidirect
11. #22610207C2semidirect
12. #22610204C2semidirect
13. #22609809C2semidirect
14. C22⋊C4×#10596831C2semidirect
15. C73×#1871C2semidirect
22. #17988826C4semidirect
23. #17988826C4semidirect
24. #17988821C4semidirect
25. #17988821C4semidirect
26. #17988818C4semidirect
27. #17988818C4semidirect
28. #17988814C4semidirect
29. #17988814C4semidirect
112. #14556526D4semidirect
353. C22×C73#443semidirect
394. #1871D73semidirect
399. C73#23018semidirect
740. C22#17988701semidirect

Maximal subgroups

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

subgroupindex
#226195092
C2×#179887012
#226186582
#226186562
C22×#145565262
#226108162
#226106782
#226105822
#226105772
#226102312
#226102072
#226102042
#226098092
C22⋊C4×#105968312
C73×#18712
#2301873