Finite Group Databasebeta

← #33088495

Subgroups — #33088495

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988634C211yesmaximal, characteristic, complemented
2C2×#104×D73C211yesmaximal, characteristic
3#22618446C211yesmaximal, characteristic
4#22618373C211yesmaximal, characteristic
5#22618347C211yesmaximal, characteristic, complemented
6#22610582C211yesmaximal, characteristic, complemented
7#22610581C211yesmaximal, characteristic, complemented
8#22610580C211yesmaximal, characteristic, complemented
9#22610579C211yesmaximal, characteristic, complemented
10#22610578C211yesmaximal, characteristic, complemented
11#22610577C211yesmaximal, characteristic, complemented
12#22610576C211yesmaximal, characteristic, complemented
13#339×D73C211yesmaximal, characteristic, complemented
14#22609623C211yesmaximal, characteristic, complemented
15C73×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19C2×M16×D73C2211yescharacteristic
20C2×M16×D73C2211yescharacteristic
21#117×D73C2211yescharacteristic
22C2×C42×D73C2211yescharacteristic
23#17988634—24no—
24C2×#14556527C2211yescharacteristic, complemented
25C2×#14556526C2211yescharacteristic, complemented
26C2×#14556526C2211yescharacteristic, complemented
27C2×#14556519C2211yescharacteristic
28C2×#14556518C2211yescharacteristic
29C2×#14556517C2211yescharacteristic
30#104×D73—24no—
31#17988594C411yescharacteristic, complemented
32#17988594C411yescharacteristic, complemented
33#17988590C411yescharacteristic, complemented
34#17988590C411yescharacteristic, complemented
35#17988587C411yescharacteristic, complemented
36#17988587C411yescharacteristic, complemented
37#17988585C411yescharacteristic, complemented
38#17988585C411yescharacteristic, complemented
39#17988584C2211yescharacteristic
40#17988583C2211yescharacteristic
41#17988581C2211yescharacteristic
42#17988555C2211yescharacteristic
43#17988554C2211yescharacteristic
44#17988553C2211yescharacteristic
45#17988552—21no—
46#17988552—21no—
47#17988549—21no—
48#17988549—21no—
49#17988545C2211yescharacteristic, complemented
50#17988544—21no—
51#17988543C2211yescharacteristic, complemented
52#17988542C2211yescharacteristic, complemented
53#17988541—21no—
54#17988539—21no—
55C4×#11924011—21no—
56#17988348C2211yescharacteristic, complemented
57#17988347C2211yescharacteristic, complemented
58#17988346C2211yescharacteristic, complemented
59#17988342C2211yescharacteristic, complemented
60#17988341C2211yescharacteristic, complemented
61#17988341C2211yescharacteristic, complemented
62C2×#108×C73C2211yescharacteristic, complemented
63C2×#104×C73C2211yescharacteristic
64#416×C73C2211yescharacteristic
65#408×C73C2211yescharacteristic
66#405×C73C2211yescharacteristic, complemented
67#339×C73C2211yescharacteristic, complemented
68#336×C73C2211yescharacteristic, complemented
69C2×#11924029C2×C411yescharacteristic
70C2×#11924028—21no—
71C2×#11924028C2311yescharacteristic
72C2×#11924027—21no—
73C2×#11924027C2×C411yescharacteristic
74#41×D73—22no—
75#41×D73—22no—
76#41×D73—22no—
77#41×D73—22no—
78C2×Q8×D73C2×C411yescharacteristic
79C2×D4×D73—21no—
80C2×D4×D73C2×C411yescharacteristic
81C22×C4×D73—21no—
82C22×C4×D73—21no—
83C22×C4×D73C2311yescharacteristic
84C2×#11924012C2311yescharacteristic
85C2×#11924012C2311yescharacteristic
86C2×#11924011—22no—
87C2×#11924011—21no—
88C2×#11924011—22no—
89C2×#11924011—22no—
90C2×#11924011—22no—
91C2×#11924011—21no—
92C2×#11924011C2×C411yescharacteristic
93C2×#11924011C2×C411yescharacteristic
94C2×#11924011C2×C411yescharacteristic
95C2×#11924011C2×C411yescharacteristic
96C2×#11924011D411yescharacteristic
97C2×#11924011D411yescharacteristic
98C2×#11924011D411yescharacteristic
99C2×#11924011D411yescharacteristic
100M16×D73—22no—
101M16×D73—22no—
102M16×D73—22no—
103M16×D73D414yes—
104C22×#10596831C2311yescharacteristic
105C22×#10596831C2311yescharacteristic
106C2×C8×D73—21no—
107C2×C8×D73—21no—
108#14556550C2311yescharacteristic
109#14556549C2×C411yescharacteristic
110#14556549C2×C411yescharacteristic
111#14556548—21no—
112#14556547—21no—
113C4⋊C4×D73C2×C411yescharacteristic
114C4⋊C4×D73C2×C411yescharacteristic
115C22⋊C4×D73—21no—
116C2×C4×Dic73—21no—
117C2×C4×Dic73C2311yescharacteristic
118C42×D73—21no—
119C42×D73—22no—
120C42×D73—22no—
121#14556527—22no—
122#14556526—22no—
123#14556526—22no—
124#14556519—22no—
125#14556518—22no—
126#14556517—22no—
127#14556516C2×C411yescharacteristic, complemented
128#14556516C2×C411yescharacteristic, complemented
129#14556515C2×C411yescharacteristic, complemented
130#14556515C2×C411yescharacteristic, complemented
131#14556514C2×C411yescharacteristic, complemented
132#14556514C2×C411yescharacteristic, complemented
133#14556513C2×C411yescharacteristic, complemented
134#14556513C2×C411yescharacteristic, complemented
135#14556512C2×C411yescharacteristic, complemented
136#14556512C2×C411yescharacteristic, complemented
137#14556511C2×C411yescharacteristic, complemented
138#14556511C2×C411yescharacteristic, complemented
139C22⋊#10596831—21no—
140C22⋊#10596831—21no—
141#14556503—21no—
142#14556503—21no—
143#14556503—21no—
144#14556503—21no—
145#14556502—21no—
146#14556501—21no—
147#14556501—21no—
148C4×#10596831—21no—
149C8×Dic73—21no—
150C8×Dic73—21no—
151C2×#41×C73C2311yescharacteristic
152C2×M16×C73C2311yescharacteristic
153C2×M16×C73C2311yescharacteristic
154C22×C8×C73C2311yescharacteristic
155C22×C8×C73C2311yescharacteristic
156#117×C73C2311yescharacteristic
157C2×C42×C73C2311yescharacteristic
158#108×C73—22no—
159#104×C73—22no—
160#103×C73C2×C411yescharacteristic, complemented
161#103×C73C2×C411yescharacteristic, complemented
162#102×C73C2×C411yescharacteristic, complemented
163#102×C73C2×C411yescharacteristic, complemented
164C22⋊C8×C73—21no—
165C22⋊C8×C73—21no—
166#97×C73—21no—
167C4×C8×C73—21no—
168C23×D73—21no—
169C23×D73#4111yescharacteristic
170#11924029—22no—
171#11924029—22no—
172#11924028—21no—
173#11924028—21no—
174#11924028—21no—
175#11924028—21no—
176#11924028—42no—
177#11924028—42no—
178#11924027—22no—
179#11924027—22no—
180#11924027—42no—
181#11924027—42no—
182C2×Dic146—21no—
183C2×Dic146C22×C411yescharacteristic
184Q8×D73—22no—
185Q8×D73—22no—
186C2×D292—21no—
187C2×D292C22×C411yescharacteristic
188C2×C22⋊D73—21no—
189C2×C22⋊D73—21no—
190C2×C22⋊D73—21no—
191D4×D73—22no—
192D4×D73—22no—
193D4×D73—42no—
194D4×D73—42no—
195C22×Dic73—21no—
196C22×Dic73—21no—
197C22×Dic73#4111yescharacteristic
198C2×C4×D73—21no—
199C2×C4×D73—21no—
200C2×C4×D73—21no—
201C2×C4×D73—21no—
202C2×C4×D73—21no—
203C2×C4×D73—42no—
204C2×C4×D73—42no—
205C2×C4×D73—42no—
206C2×C4×D73—42no—
207C2×C4×D73—42no—
208C2×C4×D73C22×C411yescharacteristic
209C2×C4×D73C22×C411yescharacteristic
210C2×C4×D73C2×D412yes—
211C2×C4×D73C2×D411yescharacteristic
212C2×C4×D73C2×D411yescharacteristic
213C2×C4×D73#4112yes—
214C2×C4×D73#4112yes—
215C2×C4×D73#4112yes—
216#11924012—21no—
217#11924012—21no—
218#11924012—21no—
219#11924012C2×D412yes—
220#11924011—22no—
221#11924011—22no—
222#11924011—22no—
223#11924011—22no—
224#11924011—24no—
225#11924011—22no—
226#11924011—22no—
227#11924011—22no—
228#11924011—22no—
229#11924011—42no—
230C2×#10596831—21no—
231C2×#10596831—21no—
232C2×#10596831—21no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831C22×C411yescharacteristic
237C2×#10596831C22×C411yescharacteristic
238C2×#10596831C2×D411yescharacteristic
239C2×#10596831C2×D411yescharacteristic
240C8×D73—24no—
241C8×D73—42no—
242C4⋊Dic73C22×C411yescharacteristic
243C4⋊Dic73C22×C411yescharacteristic
244#11924007—21no—
245#11924007—21no—
246C22⋊Dic73—21no—
247#11924005—21no—
248#11924005—21no—
249C4×Dic73—21no—
250C4×Dic73—21no—
251C4×Dic73—21no—
252C4×Dic73—21no—
253C4×Dic73—21no—
254C4×Dic73—42no—
255#41×C73—21no—
256#41×C73—21no—
257#41×C73—21no—
258#41×C73—21no—
259C2×Q8×C73C22×C411yescharacteristic
260C2×D4×C73—21no—
261C2×D4×C73C22×C411yescharacteristic
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73C2411yescharacteristic
265M16×C73—21no—
266M16×C73—21no—
267M16×C73—21no—
268M16×C73C2×D412yes—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—21no—
272C2×C8×C73—21no—
273C2×C8×C73—21no—
274C2×C8×C73—21no—
275C2×C8×C73C22×C411yescharacteristic
276C2×C8×C73C22×C411yescharacteristic
277C2×C8×C73C2×D411yescharacteristic
278C2×C8×C73C2×D411yescharacteristic
279C4⋊C4×C73C22×C411yescharacteristic
280C4⋊C4×C73C22×C411yescharacteristic
281C22⋊C4×C73—21no—
282C42×C73—21no—
283C42×C73—21no—
284C42×C73—21no—
285C23×C73—21no—
286C23×C73C2×#4111yescharacteristic
287C22×D73—21no—
288C22×D73—41no—
289C22×D73—41no—
290C22×D73—42no—
291C22×D73—81no—
292C22×D73—81no—
293C22×D73C4×D411yescharacteristic
294C22×D73C4×D411yescharacteristic
295C22×D73#12412yes—
296C22×D73#12612yes—
297Q8×C73—21no—
298Q8×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—41no—
302D4×C73—41no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73C23×C411yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C2×#4111yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C22⋊D73—41no—
318C22⋊D73—41no—
319C22⋊D73—42no—
320C22⋊D73—42no—
321C2×Dic73—22no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—42no—
328C2×Dic73C4×D411yescharacteristic
329C2×Dic73C4×D411yescharacteristic
330C2×Dic73#12412yes—
331C2×Dic73#12612yes—
332D292—21no—
333D292—21no—
334D292—42no—
335C4×D73—48no—
336C4×D73—42no—
337C4×D73—41no—
338C4×D73—41no—
339C4×D73—42no—
340C4×D73—81no—
341C4×D73—81no—
342C4×D73#11712yes—
343C4×D73#11712yes—
344C4×D73C4×D412yes—
345C4×D73C4×D412yes—
346C4×D73#12112yes—
347C4×D73#12112yes—
348C4×D73#12312yes—
349C4×D73#12312yes—
350Dic146—21no—
351Dic146—21no—
352Dic146—42no—
353C8×C73—21no—
354C8×C73—21no—
355C8×C73—22no—
356C8×C73—21no—
357C8×C73—21no—
358C8×C73—41no—
359#10596831—21no—
360#10596831—21no—
361#10596831—22no—
362#10596831—21no—
363#10596831—21no—
364#10596831—41no—
365C22×C73—21no—
366C22×C73—21no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73C2×C4×D411yescharacteristic
371C22×C73C2×#12411yescharacteristic
372C22×C73C2×#12611yescharacteristic
373C2×D73—21no—
374C2×D73—21no—
375C2×D73—21no—
376C2×D73—21no—
377C2×D73—42no—
378C2×D73—42no—
379C2×D73—41no—
380C2×D73—41no—
381C2×D73—41no—
382C2×D73—84no—
383C2×D73#38812yes—
384C2×D73#38812yes—
385C4×C73—42no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73—41no—
389C4×C73C2×#11711yescharacteristic
390C4×C73C2×C4×D411yescharacteristic
391C4×C73C2×#12111yescharacteristic
392C4×C73C2×#12311yescharacteristic
393Dic73—42no—
394Dic73—41no—
395Dic73—41no—
396Dic73—41no—
397Dic73#38812yes—
398Dic73#38812yes—
399#21071—731nomaximal, Sylow
400C2×C73—21no—
401C2×C73—21no—
402C2×C73—81no—
403C2×C73C2×#38811yescharacteristic
404C2×C73#295611yescharacteristic
405C2×C73#295611yescharacteristic
406D73—22no—
407D73—22no—
408D73—81no—
409C2×#430—731no—
410C22×#104—731no—
411#2896—731no—
412#2879—731no—
413#2873—731no—
414#1929—731no—
415#1929—731no—
416#1929—731no—
417#1929—731no—
418#1929—731no—
419#1929—731no—
420#1929—731no—
421#1929D7311yescharacteristic, complemented
422C2×#339—731no—
423#1728—731no—
424C73#2107111yescharacteristic, complemented, Sylow
425C22×#41—731no—
426C22×M16—731no—
427C22×M16—731no—
428C22×M16—731no—
429C22×M16—731no—
430C2×#117—731no—
431C22×C42—731no—
432#430—1464no—
433C2×#108—731no—
434C2×#108—731no—
435C2×#108—731no—
436C2×#108C2×D7311yescharacteristic, complemented
437C2×#104—731no—
438C2×#104—731no—
439C2×#104—731no—
440C2×#104—1464no—
441C2×#104C2×D7311yescharacteristic
442#419—731no—
443#419—731no—
444#418—731no—
445#418—731no—
446#417—731no—
447#417—731no—
448#417—731no—
449#417—731no—
450#416—731no—
451#416—731no—
452#416—731no—
453#416C2×D7311yescharacteristic
454#408—731no—
455#408—731no—
456#408—731no—
457#408—1461no—
458#408—1461no—
459#408C2×D7311yescharacteristic
460#407—1461no—
461#407—1461no—
462#405—731no—
463#405—731no—
464#405—731no—
465#405—1461no—
466#405—1461no—
467#405C2×D7311yescharacteristic, complemented
468C4×M16—1461no—
469C4×M16—1461no—
470#339—731no—
471#339—731no—
472#339—731no—
473#339C2×D7311yescharacteristic, complemented
474#336—731no—
475#336—731no—
476#336—731no—
477#336C2×D7311yescharacteristic, complemented
478C2×#41—731no—
479C2×#41—731no—
480C2×#41—731no—
481C2×#41—1461no—
482C2×#41—1462no—
483C2×#41—1462no—
484C2×#41—1462no—
485C2×#41—1462no—
486C2×#41—1461no—
487C2×#41C22×D7311yescharacteristic
488C22×Q8—731no—
489C22×D4—731no—
490C22×D4—1461no—
491C23×C4—731no—
492C23×C4—1461no—
493C23×C4—1461no—
494C2×M16—731no—
495C2×M16—731no—
496C2×M16—731no—
497C2×M16—731no—
498C2×M16—731no—
499C2×M16—731no—
500C2×M16—731no—
501C2×M16—731no—
502C2×M16—731no—
503C2×M16—734no—
504C2×M16—731no—
505C2×M16—1461no—
506C2×M16—1461no—
507C2×M16—1462no—
508C2×M16—1462no—
509C2×M16—1462no—
510C2×M16—1462no—
511C2×M16—1462no—
512C2×M16—1462no—
513C2×M16—1462no—
514C2×M16C22×D7311yescharacteristic
515C2×M16C22×D7311yescharacteristic
516C22×C8—731no—
517C22×C8—731no—
518C22×C8—1461no—
519C22×C8—1461no—
520C22×C8C22×D7311yescharacteristic
521C22×C8C22×D7311yescharacteristic
522#117—731no—
523#117—731no—
524#117—731no—
525#117—1461no—
526#117—1461no—
527#117C22×D7311yescharacteristic
528C2×C4⋊C4—731no—
529C2×C4⋊C4—731no—
530C2×C22⋊C4—1461no—
531C2×C42—731no—
532C2×C42—1462no—
533C2×C42—1462no—
534C2×C42—1461no—
535C2×C42—1461no—
536C2×C42C22×D7311yescharacteristic
537#108—22no—
538#108—1462no—
539#108—1462no—
540#108—1462no—
541#104—22no—
542#104—1462no—
543#104—1462no—
544#104—1462no—
545#103—731no—
546#103—731no—
547#103—731no—
548#103—731no—
549#103—731no—
550#103—731no—
551#103C4×D7311yescharacteristic, complemented
552#103C4×D7311yescharacteristic, complemented
553#102—731no—
554#102—731no—
555#102—731no—
556#102—731no—
557#102—731no—
558#102—731no—
559#102C4×D7311yescharacteristic, complemented
560#102C4×D7311yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—1461no—
564C22⋊C8—1461no—
565C22⋊C8—1461no—
566C22⋊C8—1461no—
567C22⋊C8—1461no—
568C22⋊C8—1461no—
569#97—21no—
570#97—1461no—
571#97—1461no—
572#97—1461no—
573C4×C8—21no—
574C4×C8—1461no—
575C4×C8—1461no—
576C4×C8—1461no—
577C24—731no—
578C24—1461no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—2922no—
584#41—2922no—
585#41—2922no—
586#41—2922no—
587#41—1462no—
588#41—1462no—
589#41—1462no—
590#41—1462no—
591#41—1461no—
592#41—1461no—
593#41—1461no—
594#41—1461no—
595C2×Q8—731no—
596C2×Q8—1461no—
597C2×Q8—1462no—
598C2×Q8—1462no—
599C2×Q8C2×C4×D7311yescharacteristic
600C2×D4—21no—
601C2×D4—2922no—
602C2×D4—2922no—
603C2×D4—731no—
604C2×D4—1461no—
605C2×D4—1462no—
606C2×D4—1462no—
607C2×D4—1461no—
608C2×D4—1461no—
609C2×D4—1461no—
610C2×D4C2×C4×D7311yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—2922no—
614C22×C4—2922no—
615C22×C4—2922no—
616C22×C4—2922no—
617C22×C4—2922no—
618C22×C4—731no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—732no—
622C22×C4—731no—
623C22×C4—731no—
624C22×C4—732no—
625C22×C4—732no—
626C22×C4—732no—
627C22×C4—1461no—
628C22×C4—1461no—
629C22×C4—1461no—
630C22×C4—1461no—
631C22×C4—1461no—
632C22×C4—1461no—
633C22×C4—1461no—
634C22×C4C23×D7311yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—2922no—
639M16—732no—
640M16—1462no—
641M16—1462no—
642M16—1462no—
643M16—1462no—
644M16—1464no—
645M16—1462no—
646M16—1462no—
647M16—1462no—
648M16—1462no—
649M16—1461no—
650M16—1461no—
651M16—1461no—
652M16D4×D7312yes—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—2922no—
660C2×C8—731no—
661C2×C8—731no—
662C2×C8—731no—
663C2×C8—731no—
664C2×C8—1464no—
665C2×C8—1461no—
666C2×C8—1461no—
667C2×C8—1461no—
668C2×C8—1461no—
669C2×C8—1461no—
670C2×C8—1461no—
671C2×C8C2×C4×D7311yescharacteristic
672C2×C8C2×C4×D7311yescharacteristic
673C2×C8D4×D7311yescharacteristic
674C2×C8D4×D7311yescharacteristic
675C4⋊C4—731no—
676C4⋊C4—731no—
677C4⋊C4—1461no—
678C4⋊C4—1461no—
679C4⋊C4C2×C4×D7311yescharacteristic
680C4⋊C4C2×C4×D7311yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—1461no—
683C22⋊C4—1461no—
684C22⋊C4—1461no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—2922no—
689C42—1461no—
690C42—1461no—
691C42—1461no—
692C42—1461no—
693C42—1461no—
694C23—21no—
695C23—2921no—
696C23—2921no—
697C23—2922no—
698C23—5841no—
699C23—5841no—
700C23—732no—
701C23—732no—
702C23—731no—
703C23—731no—
704C23—1461no—
705C23#41×D7311yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—2922no—
709Q8—1461no—
710Q8—1461no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—2922no—
716D4—2922no—
717D4—2921no—
718D4—2921no—
719D4—2922no—
720D4—1461no—
721D4—1461no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—2928no—
731C2×C4—2922no—
732C2×C4—2922no—
733C2×C4—2921no—
734C2×C4—2921no—
735C2×C4—2922no—
736C2×C4—2921no—
737C2×C4—2921no—
738C2×C4—5841no—
739C2×C4—5841no—
740C2×C4—731no—
741C2×C4—731no—
742C2×C4—732no—
743C2×C4—732no—
744C2×C4—732no—
745C2×C4—732no—
746C2×C4—732no—
747C2×C4—732no—
748C2×C4—732no—
749C2×C4—732no—
750C2×C4—732no—
751C2×C4—732no—
752C2×C4—1462no—
753C2×C4—1461no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4C22×C4×D7311yescharacteristic
757C2×C4C2×D4×D7311yescharacteristic
758C2×C4C2×D4×D7311yescharacteristic
759C2×C4#41×D7311yescharacteristic
760C2×C4#41×D7311yescharacteristic
761C2×C4#41×D7311yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—2921no—
769C8—1461no—
770C8—1461no—
771C8—1462no—
772C8—1461no—
773C8—1461no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—2922no—
780C22—2922no—
781C22—2921no—
782C22—2921no—
783C22—2921no—
784C22—5844no—
785C22—732no—
786C22—732no—
787C22—1461no—
788C22—1461no—
789C22—1461no—
790C22—1461no—
791C22C4×D4×D7311yescharacteristic
792C22#124×D7311yescharacteristic
793C22#126×D7311yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—2922no—
799C4—2921no—
800C4—2921no—
801C4—2921no—
802C4—732no—
803C4—732no—
804C4#117×D7311yescharacteristic
805C4C4×D4×D7311yescharacteristic
806C4#121×D7311yescharacteristic
807C4#123×D7311yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—5841no—
812C2—1462no—
813C2—1462no—
814C2#388×D7311yescharacteristic
815C2#2261883611yescharacteristic
816C2#2261883911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1929C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×D73C22
cosocleC22×C4×C73C24
hypercenter#1929D73
hypocenterC73#21071
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#17988634C2semidirect
5. #22618347C2semidirect
6. #22610582C2semidirect
7. #22610581C2semidirect
8. #22610580C2semidirect
9. #22610579C2semidirect
10. #22610578C2semidirect
11. #22610577C2semidirect
12. #22610576C2semidirect
13. #339×D73C2semidirect
14. #22609623C2semidirect
15. C73×#1929C2semidirect
24. C2×#14556527C22semidirect
25. C2×#14556526C22semidirect
26. C2×#14556526C22semidirect
31. #17988594C4semidirect
32. #17988594C4semidirect
33. #17988590C4semidirect
34. #17988590C4semidirect
35. #17988587C4semidirect
36. #17988587C4semidirect
37. #17988585C4semidirect
38. #17988585C4semidirect
49. #17988545C22semidirect
51. #17988543C22semidirect
52. #17988542C22semidirect
56. #17988348C22semidirect
57. #17988347C22semidirect
58. #17988346C22semidirect
59. #17988342C22semidirect
60. #17988341C22semidirect
61. #17988341C22semidirect
62. C2×#108×C73C22semidirect
66. #405×C73C22semidirect
67. #339×C73C22semidirect
68. #336×C73C22semidirect
127. #14556516C2×C4semidirect
128. #14556516C2×C4semidirect
129. #14556515C2×C4semidirect
130. #14556515C2×C4semidirect
131. #14556514C2×C4semidirect
132. #14556514C2×C4semidirect
133. #14556513C2×C4semidirect
134. #14556513C2×C4semidirect
135. #14556512C2×C4semidirect
136. #14556512C2×C4semidirect
137. #14556511C2×C4semidirect
138. #14556511C2×C4semidirect
160. #103×C73C2×C4semidirect
161. #103×C73C2×C4semidirect
162. #102×C73C2×C4semidirect
163. #102×C73C2×C4semidirect
421. #1929D73semidirect
424. C73#21071semidirect
436. C2×#108C2×D73semidirect
467. #405C2×D73semidirect
473. #339C2×D73semidirect
477. #336C2×D73semidirect
551. #103C4×D73semidirect
552. #103C4×D73semidirect
559. #102C4×D73semidirect
560. #102C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179886342
C2×#104×D732
#226184462
#226183732
#226183472
#226105822
#226105812
#226105802
#226105792
#226105782
#226105772
#226105762
#339×D732
#226096232
C73×#19292
#2107173