Finite Group Databasebeta

← #33106750

Subgroups — #33106750

Order 18688.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619145C211yesmaximal, characteristic
2C2×#17988701C211yesmaximal, characteristic, complemented
3#22618661C211yesmaximal, characteristic, complemented
4C2×#104×D73C211yesmaximal, characteristic, complemented
5#22618379C211yesmaximal, characteristic, complemented
6#22610632C211yesmaximal, characteristic, complemented
7#22610576C211yesmaximal, characteristic, complemented
8#22610371C211yesmaximal, characteristic, complemented
9#22610261C211yesmaximal, characteristic, complemented
10#22610260C211yesmaximal, characteristic, complemented
11#22610203C211yesmaximal, characteristic, complemented
12#22610134C211yesmaximal, characteristic, complemented
13#22609768C211yesmaximal, characteristic, complemented
14C4×#14556503C211yesmaximal, characteristic, complemented
15C73×#1974C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556599C2211yescharacteristic
19C2×#14556598C2211yescharacteristic, complemented
20C2×#14556597C2211yescharacteristic
21C2×M16×D73C2211yescharacteristic
22#17989094C2211yescharacteristic
23C2×C42×D73C2211yescharacteristic
24#17988748C411yescharacteristic, complemented
25#17988746C411yescharacteristic, complemented
26#17988741C411yescharacteristic, complemented
27#17988736C411yescharacteristic, complemented
28#17988731C411yescharacteristic, complemented
29#17988729C411yescharacteristic, complemented
30#17988724C411yescharacteristic, complemented
31#17988719C411yescharacteristic, complemented
32#17988701—24no—
33#17988662—21no—
34#17988661—21no—
35#17988655—21no—
36#17988650—21no—
37C2×#14556526C2211yescharacteristic, complemented
38#17988615C2211yescharacteristic, complemented
39C2×#14556519C2211yescharacteristic
40C2×#14556518C2211yescharacteristic
41C2×#14556518C2211yescharacteristic, complemented
42C2×#14556517C2211yescharacteristic
43#104×D73—24no—
44#17988584C2211yescharacteristic
45#17988583C2211yescharacteristic
46#17988554C2211yescharacteristic
47#17988552—21no—
48#17988552—21no—
49#17988550C2211yescharacteristic
50#17988549—21no—
51C2×#14556503C2211yescharacteristic
52C2×#14556503C2211yescharacteristic
53C22⋊C8×D73—21no—
54#17988542C2211yescharacteristic, complemented
55C2×C4×#10596831C2211yescharacteristic, complemented
56#17988352C2211yescharacteristic, complemented
57#17988351C2211yescharacteristic, complemented
58#17988348C2211yescharacteristic, complemented
59#17988347C2211yescharacteristic, complemented
60#17988341C2211yescharacteristic, complemented
61#17988341C2211yescharacteristic, complemented
62C2×#135×C73C2211yescharacteristic
63C2×#108×C73C2211yescharacteristic, complemented
64C2×#104×C73C2211yescharacteristic
65C2×#104×C73C2211yescharacteristic, complemented
66#408×C73C2211yescharacteristic
67#408×C73C2211yescharacteristic, complemented
68C2×C4×C8×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—41no—
77#41×D73—41no—
78C2×Q8×D73C2×C411yescharacteristic
79C2×D4×D73—21no—
80C2×D4×D73C2×C411yescharacteristic
81C22×C4×D73—21no—
82C22×C4×D73—21no—
83C22×C4×D73C2311yescharacteristic
84#14556611—22no—
85#14556611—22no—
86C2×#11924018C2×C411yescharacteristic, complemented
87C2×#11924016C2×C411yescharacteristic, complemented
88C2×#11924015C2×C411yescharacteristic, complemented
89C2×#11924013C2×C411yescharacteristic, complemented
90#14556599—22no—
91#14556599—41no—
92#14556598—22no—
93#14556598—41no—
94#14556597—22no—
95#14556597—41no—
96C2×#11924012—21no—
97C2×#11924012C2311yescharacteristic
98C2×#11924012C2311yescharacteristic
99C2×#11924011—21no—
100C2×#11924011—21no—
101C2×#11924011—21no—
102M16×D73—22no—
103M16×D73—41no—
104C22×#10596831—21no—
105C22×#10596831C2311yescharacteristic
106C22×#10596831C2311yescharacteristic
107C2×C8×D73—21no—
108C2×C8×D73—21no—
109C2×C8×D73—21no—
110#14556572—21no—
111#14556567C2×C411yescharacteristic
112#14556567C2×C411yescharacteristic
113#14556562C2×C411yescharacteristic
114#14556562C2×C411yescharacteristic
115#14556559—21no—
116C4×C22⋊D73—21no—
117C4×C22⋊D73—21no—
118#14556550C2311yescharacteristic
119C2×C4×Dic73—21no—
120C2×C4×Dic73C2311yescharacteristic
121C42×D73—22no—
122C42×D73—41no—
123#14556526—22no—
124#14556520—21no—
125#14556520—21no—
126#14556519D414yescomplemented
127#14556518—22no—
128#14556518—41no—
129#14556517—22no—
130#14556516C2×C411yescharacteristic, complemented
131#14556516C2×C411yescharacteristic, complemented
132#14556515C2×C411yescharacteristic, complemented
133#14556515C2×C411yescharacteristic, complemented
134#14556513C2×C411yescharacteristic, complemented
135#14556513C2×C411yescharacteristic, complemented
136#14556512C2×C411yescharacteristic, complemented
137#14556512C2×C411yescharacteristic, complemented
138C22⋊#10596831—21no—
139C22⋊#10596831—21no—
140#14556503—21no—
141#14556503—21no—
142#14556503C2×C411yescharacteristic
143#14556503C2×C411yescharacteristic
144#14556503C2×C411yescharacteristic
145#14556503C2×C411yescharacteristic
146#14556503D411yescharacteristic
147#14556503D411yescharacteristic
148#14556503D411yescharacteristic
149#14556503D411yescharacteristic
150#14556501—21no—
151C4×#10596831—22no—
152C8×Dic73—21no—
153C2×#41×C73C2311yescharacteristic
154C2×#41×C73C2311yescharacteristic
155#135×C73—41no—
156#135×C73—41no—
157C2×Q16×C73C2×C411yescharacteristic, complemented
158C2×SD16×C73C2×C411yescharacteristic, complemented
159C2×SD16×C73C2×C411yescharacteristic, complemented
160C2×D8×C73C2×C411yescharacteristic, complemented
161C2×M16×C73C2311yescharacteristic
162C2×M16×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C2×C42×C73C2311yescharacteristic
166#108×C73—41no—
167#104×C73—22no—
168#104×C73—22no—
169C22⋊C8×C73—21no—
170C22⋊C8×C73—21no—
171C22⋊C8×C73—21no—
172C22⋊C8×C73—21no—
173C4×C8×C73—41no—
174C23×D73—21no—
175C23×D73#4111yescharacteristic
176#11924029—22no—
177#11924029—41no—
178#11924028—21no—
179#11924028—21no—
180#11924028—42no—
181#11924028—42no—
182#11924028C2×D412yes—
183#11924028#4112yes—
184#11924027—22no—
185#11924027—41no—
186#11924027—42no—
187#11924027—42no—
188C2×Dic146—21no—
189C2×Dic146C22×C411yescharacteristic
190Q8×D73—22no—
191Q8×D73—41no—
192C2×D292—21no—
193C2×D292C22×C411yescharacteristic
194C2×C22⋊D73—21no—
195C2×C22⋊D73—21no—
196C2×C22⋊D73—21no—
197C2×C22⋊D73—21no—
198C2×C22⋊D73—21no—
199D4×D73—22no—
200D4×D73—41no—
201D4×D73—42no—
202D4×D73—42no—
203C22×Dic73—21no—
204C22×Dic73—21no—
205C22×Dic73#4111yescharacteristic
206C2×C4×D73—21no—
207C2×C4×D73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—24no—
212C2×C4×D73—21no—
213C2×C4×D73—21no—
214C2×C4×D73—42no—
215C2×C4×D73—42no—
216C2×C4×D73—42no—
217C2×C4×D73—42no—
218C2×C4×D73C22×C411yescharacteristic
219C2×C4×D73C22×C411yescharacteristic
220C2×C4×D73C2×D411yescharacteristic
221C2×C4×D73C2×D411yescharacteristic
222#11924018—22no—
223#11924016—22no—
224#11924015—22no—
225#11924013—22no—
226#11924012—21no—
227#11924012—21no—
228#11924012—21no—
229#11924012—42no—
230#11924012C2×D412yes—
231#11924011—42no—
232#11924011—42no—
233#11924011—42no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831—21no—
237C2×#10596831—21no—
238C2×#10596831—21no—
239C2×#10596831—21no—
240C2×#10596831—42no—
241C2×#10596831C22×C411yescharacteristic
242C2×#10596831C22×C411yescharacteristic
243C2×#10596831C2×D411yescharacteristic
244C2×#10596831C2×D411yescharacteristic
245C8×D73—42no—
246C8×D73—42no—
247C8×D73—42no—
248C4⋊Dic73C22×C411yescharacteristic
249C4⋊Dic73C22×C411yescharacteristic
250#11924007—21no—
251#11924007—21no—
252C22⋊Dic73—21no—
253C22⋊Dic73—21no—
254C22⋊Dic73—21no—
255#11924005—21no—
256#11924005—21no—
257C4×Dic73—21no—
258C4×Dic73—21no—
259C4×Dic73—21no—
260C4×Dic73—42no—
261#41×C73—21no—
262#41×C73—21no—
263#41×C73—21no—
264#41×C73—21no—
265#41×C73—21no—
266#41×C73—21no—
267#41×C73—21no—
268#41×C73—21no—
269C2×Q8×C73C22×C411yescharacteristic
270C2×Q8×C73C22×C411yescharacteristic
271C2×D4×C73—21no—
272C2×D4×C73—21no—
273C2×D4×C73C22×C411yescharacteristic
274C2×D4×C73C22×C411yescharacteristic
275C22×C4×C73—21no—
276C22×C4×C73—21no—
277C22×C4×C73—21no—
278C22×C4×C73C2411yescharacteristic
279Q16×C73—41no—
280SD16×C73—41no—
281SD16×C73—41no—
282D8×C73—41no—
283M16×C73—21no—
284M16×C73—21no—
285M16×C73—21no—
286M16×C73—21no—
287C2×C8×C73—21no—
288C2×C8×C73—21no—
289C2×C8×C73—21no—
290C2×C8×C73—21no—
291C2×C8×C73—21no—
292C2×C8×C73—21no—
293C2×C8×C73C22×C411yescharacteristic
294C2×C8×C73C22×C411yescharacteristic
295C2×C8×C73C2×D411yescharacteristic
296C2×C8×C73C2×D411yescharacteristic
297C42×C73—21no—
298C42×C73C2×D412yes—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73C2×#4111yescharacteristic
302C22×D73—21no—
303C22×D73—21no—
304C22×D73—21no—
305C22×D73—22no—
306C22×D73—41no—
307C22×D73—42no—
308C22×D73—42no—
309C22×D73—81no—
310C22×D73C4×D411yescharacteristic
311C22×D73C4×D411yescharacteristic
312Q8×C73—21no—
313Q8×C73—21no—
314Q8×C73—21no—
315Q8×C73—21no—
316D4×C73—21no—
317D4×C73—21no—
318D4×C73—21no—
319D4×C73—21no—
320D4×C73—41no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73—41no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73C23×C411yescharacteristic
334C2×C4×C73C22×D411yescharacteristic
335C2×C4×C73C22×D411yescharacteristic
336C2×C4×C73C2×#4111yescharacteristic
337C2×C4×C73H(5,𝔽2)11yescharacteristic
338C2×C4×C73H(5,𝔽2)11yescharacteristic
339C22⋊D73—22no—
340C22⋊D73—22no—
341C22⋊D73—42no—
342C22⋊D73—42no—
343C22⋊D73—42no—
344C22⋊D73—81no—
345C2×Dic73—21no—
346C2×Dic73—21no—
347C2×Dic73—21no—
348C2×Dic73—22no—
349C2×Dic73—21no—
350C2×Dic73—21no—
351C2×Dic73—42no—
352C2×Dic73—41no—
353C2×Dic73—41no—
354C2×Dic73C4×D411yescharacteristic
355C2×Dic73C4×D411yescharacteristic
356D292—21no—
357D292—42no—
358D292C4×D412yes—
359C4×D73—21no—
360C4×D73—21no—
361C4×D73—21no—
362C4×D73—21no—
363C4×D73—21no—
364C4×D73—22no—
365C4×D73—21no—
366C4×D73—22no—
367C4×D73—21no—
368C4×D73—21no—
369C4×D73—42no—
370C4×D73—42no—
371C4×D73—48no—
372Dic146—21no—
373Dic146—42no—
374Dic146C4×D412yes—
375C8×C73—21no—
376C8×C73—21no—
377C8×C73—21no—
378C8×C73—21no—
379C8×C73—41no—
380C8×C73—41no—
381#10596831—21no—
382#10596831—21no—
383#10596831—21no—
384#10596831—22no—
385#10596831—21no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—41no—
390C22×C73—41no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73C2×C4×D411yescharacteristic
396C22×C73#54611yescharacteristic
397C22×C73#55111yescharacteristic
398C2×D73—21no—
399C2×D73—21no—
400C2×D73—21no—
401C2×D73—22no—
402C2×D73—21no—
403C2×D73—21no—
404C2×D73—42no—
405C2×D73—42no—
406C2×D73—41no—
407C2×D73—41no—
408C2×D73—84no—
409C2×D73#44312yescomplemented
410C4×C73—24no—
411C4×C73—41no—
412C4×C73—41no—
413C4×C73C2×C4×D411yescharacteristic
414C4×C73#51811yescharacteristic
415C4×C73D4211yescharacteristic
416C4×C73#54611yescharacteristic
417Dic73—22no—
418Dic73—21no—
419Dic73—21no—
420Dic73—42no—
421Dic73—41no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—21no—
426C2×C73—81no—
427C2×C73—81no—
428C2×C73#235811yescharacteristic
429C2×C73C2×#44311yescharacteristic
430C2×C73#295611yescharacteristic
431D73—22no—
432D73—41no—
433D73—42no—
434#3002—731no—
435C2×#443—731no—
436#2933—731no—
437C22×#104—731no—
438#2880—731no—
439#1974D7311yescharacteristic, complemented
440#1937—731no—
441#1929—731no—
442#1896—731no—
443#1876—731no—
444#1876—731no—
445#1866—731no—
446#1855—731no—
447#1764—731no—
448C4×C22⋊C8—731no—
449C73#2288811yescharacteristic, complemented, Sylow
450C22×#41—731no—
451C2×#135—731no—
452C2×#135C2×D7311yescharacteristic
453C2×#131—731no—
454C2×#131—731no—
455C2×#131—731no—
456C22×M16—731no—
457#525—731no—
458C22×C42—731no—
459#452—731no—
460#452—731no—
461#451—731no—
462#450—731no—
463#449—731no—
464#449—731no—
465#448—731no—
466#447—731no—
467#443—1464no—
468#436—1461no—
469#435—1461no—
470#435—1461no—
471C8×D4—1461no—
472C2×#108—731no—
473C2×#108C2×D7311yescharacteristic, complemented
474#424—731no—
475C2×#104—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479C2×#104—1464no—
480C2×#104C2×D7311yescharacteristic
481C2×#104C2×D7311yescharacteristic, complemented
482#416—731no—
483#416—731no—
484#408—731no—
485#408—1461no—
486#408—1461no—
487#408C2×D7311yescharacteristic
488#408C2×D7311yescharacteristic, complemented
489#407—731no—
490#407—1461no—
491C2×C22⋊C8—731no—
492C2×C22⋊C8—731no—
493C2×C22⋊C8—1461no—
494#405—731no—
495C2×C4×C8—731no—
496C2×C4×C8C2×D7311yescharacteristic, complemented
497#341—731no—
498#341—731no—
499#339—731no—
500#339—731no—
501#336—731no—
502#336—731no—
503C2×#41—2921no—
504C2×#41—2921no—
505C2×#41—731no—
506C2×#41—731no—
507C2×#41—731no—
508C2×#41—1461no—
509C2×#41—1462no—
510C2×#41—1462no—
511C2×#41—1461no—
512C2×#41C22×D7311yescharacteristic
513C2×#41C22×D7311yescharacteristic
514C22×Q8—731no—
515C22×D4—731no—
516C22×D4—1461no—
517C23×C4—731no—
518C23×C4—1461no—
519C23×C4—1461no—
520#135—41no—
521#135—41no—
522#135—1462no—
523#135—1462no—
524C2×Q16—731no—
525C2×Q16C4×D7311yescharacteristic, complemented
526C2×SD16—731no—
527C2×SD16—731no—
528C2×SD16C4×D7311yescharacteristic, complemented
529C2×SD16C4×D7311yescharacteristic, complemented
530C2×D8—731no—
531C2×D8C4×D7311yescharacteristic, complemented
532#131—2921no—
533#131—2921no—
534#131—2921no—
535#131—1462no—
536#131—1462no—
537#131—1462no—
538C2×M16—2921no—
539C2×M16—731no—
540C2×M16—731no—
541C2×M16—1461no—
542C2×M16—1461no—
543C2×M16—1462no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—731no—
549C22×C8—731no—
550C22×C8—1461no—
551C22×C8—1461no—
552C22×C8—1461no—
553C22×C8—1461no—
554C22×C8C22×D7311yescharacteristic
555C22×C8C22×D7311yescharacteristic
556#123—1461no—
557C22⋊Q8—731no—
558C22⋊Q8—731no—
559#121—731no—
560#121—731no—
561#120—1461no—
562C4×D4—1461no—
563C4×D4—1461no—
564#117—731no—
565C2×C42—2921no—
566C2×C42—731no—
567C2×C42—1461no—
568C2×C42—1462no—
569C2×C42C22×D7311yescharacteristic
570#108—41no—
571#108—1462no—
572C4⋊C8—1461no—
573C4⋊C8—1461no—
574#104—22no—
575#104—22no—
576#104—2921no—
577#104—734no—
578#104—1462no—
579#104—1462no—
580#103—731no—
581#103—731no—
582#103—731no—
583#103—731no—
584#102—731no—
585#102—731no—
586#102—731no—
587#102—731no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—731no—
593C22⋊C8—731no—
594C22⋊C8—731no—
595C22⋊C8—731no—
596C22⋊C8—731no—
597C22⋊C8—731no—
598C22⋊C8—731no—
599C22⋊C8—731no—
600C22⋊C8—1461no—
601C22⋊C8—1461no—
602C22⋊C8—1461no—
603C22⋊C8—1461no—
604#97—1461no—
605C4×C8—41no—
606C4×C8—1461no—
607C4×C8—1462no—
608C24—731no—
609C24—1461no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—2922no—
619#41—2922no—
620#41—2921no—
621#41—2922no—
622#41—2922no—
623#41—2921no—
624#41—732no—
625#41—732no—
626#41—1462no—
627#41—1462no—
628#41—1461no—
629#41—1461no—
630C2×Q8—2921no—
631C2×Q8—731no—
632C2×Q8—1461no—
633C2×Q8—1462no—
634C2×Q8C2×C4×D7311yescharacteristic
635C2×Q8C2×C4×D7311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—2922no—
639C2×D4—2922no—
640C2×D4—2921no—
641C2×D4—731no—
642C2×D4—1461no—
643C2×D4—1461no—
644C2×D4—1462no—
645C2×D4—1461no—
646C2×D4—1461no—
647C2×D4—1461no—
648C2×D4—1461no—
649C2×D4C2×C4×D7311yescharacteristic
650C2×D4C2×C4×D7311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—2922no—
655C22×C4—2922no—
656C22×C4—2922no—
657C22×C4—2922no—
658C22×C4—731no—
659C22×C4—731no—
660C22×C4—731no—
661C22×C4—731no—
662C22×C4—731no—
663C22×C4—1461no—
664C22×C4—1461no—
665C22×C4—1464no—
666C22×C4—1461no—
667C22×C4—1461no—
668C22×C4—1461no—
669C22×C4—1461no—
670C22×C4—1461no—
671C22×C4—1461no—
672C22×C4—1461no—
673C22×C4C23×D7311yescharacteristic
674Q16—41no—
675Q16—1462no—
676SD16—41no—
677SD16—41no—
678SD16—1462no—
679SD16—1462no—
680D8—41no—
681D8—1462no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—2922no—
687M16—2922no—
688M16—2922no—
689M16—2922no—
690M16—732no—
691M16—1461no—
692M16—1461no—
693M16—1461no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—2922no—
701C2×C8—2922no—
702C2×C8—2922no—
703C2×C8—2922no—
704C2×C8—731no—
705C2×C8—731no—
706C2×C8—731no—
707C2×C8—731no—
708C2×C8—1461no—
709C2×C8—1461no—
710C2×C8—1461no—
711C2×C8—1461no—
712C2×C8—1461no—
713C2×C8—1461no—
714C2×C8C2×C4×D7311yescharacteristic
715C2×C8C2×C4×D7311yescharacteristic
716C2×C8D4×D7311yescharacteristic
717C2×C8D4×D7311yescharacteristic
718C4⋊C4—731no—
719C4⋊C4—731no—
720C4⋊C4—1461no—
721C4⋊C4—1461no—
722C22⋊C4—1461no—
723C22⋊C4—1461no—
724C22⋊C4—1461no—
725C22⋊C4—1461no—
726C22⋊C4—1461no—
727C42—21no—
728C42—2922no—
729C42—1461no—
730C42—1461no—
731C42—1461no—
732C42D4×D7312yes—
733C23—21no—
734C23—21no—
735C23—2921no—
736C23—2922no—
737C23—2922no—
738C23—5841no—
739C23—731no—
740C23—731no—
741C23—1462no—
742C23—1461no—
743C23—1461no—
744C23—1461no—
745C23#41×D7311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—2922no—
751Q8—732no—
752Q8—1461no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—2922no—
762D4—2922no—
763D4—2922no—
764D4—2922no—
765D4—5841no—
766D4—732no—
767D4—1462no—
768D4—1462no—
769D4—1461no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—2928no—
780C2×C4—2922no—
781C2×C4—2922no—
782C2×C4—2921no—
783C2×C4—2921no—
784C2×C4—2922no—
785C2×C4—731no—
786C2×C4—731no—
787C2×C4—1462no—
788C2×C4—1461no—
789C2×C4—1461no—
790C2×C4—1461no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1462no—
795C2×C4—1461no—
796C2×C4—1462no—
797C2×C4—1461no—
798C2×C4—1461no—
799C2×C4—1461no—
800C2×C4—1461no—
801C2×C4—1461no—
802C2×C4—1461no—
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C2×D4×D7311yescharacteristic
806C2×C4#41×D7311yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663611yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—2921no—
816C8—1461no—
817C8—1462no—
818C8—1461no—
819C8—1461no—
820C8—1461no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—2922no—
830C22—2922no—
831C22—2921no—
832C22—2921no—
833C22—5844no—
834C22—732no—
835C22—1462no—
836C22—1461no—
837C22—1461no—
838C22—1461no—
839C22—1461no—
840C22—1461no—
841C22C4×D4×D7311yescharacteristic
842C22#1798922611yescharacteristic
843C22#1798926711yescharacteristic
844C4—24no—
845C4—41no—
846C4—41no—
847C4—2922no—
848C4—2921no—
849C4—2921no—
850C4—1461no—
851C4—1462no—
852C4—1461no—
853C4C4×D4×D7311yescharacteristic
854C4#1798906011yescharacteristic
855C4#1798922211yescharacteristic
856C4#1798922611yescharacteristic
857C2—21no—
858C2—21no—
859C2—81no—
860C2—81no—
861C2—2921no—
862C2—2922no—
863C2—1462no—
864C2#2261291211yescharacteristic
865C2#443×D7311yescharacteristic
866C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1974C2
socleC22×C73C2×C4×D4
prime radical#22619145C2
cosocleC22×C4×C73C24
hypercenter#1974D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
2. C2×#17988701C2semidirect
3. #22618661C2semidirect
4. C2×#104×D73C2semidirect
5. #22618379C2semidirect
6. #22610632C2semidirect
7. #22610576C2semidirect
8. #22610371C2semidirect
9. #22610261C2semidirect
10. #22610260C2semidirect
11. #22610203C2semidirect
12. #22610134C2semidirect
13. #22609768C2semidirect
14. C4×#14556503C2semidirect
15. C73×#1974C2semidirect
19. C2×#14556598C22semidirect
24. #17988748C4semidirect
25. #17988746C4semidirect
26. #17988741C4semidirect
27. #17988736C4semidirect
28. #17988731C4semidirect
29. #17988729C4semidirect
30. #17988724C4semidirect
31. #17988719C4semidirect
37. C2×#14556526C22semidirect
38. #17988615C22semidirect
41. C2×#14556518C22semidirect
54. #17988542C22semidirect
55. C2×C4×#10596831C22semidirect
56. #17988352C22semidirect
57. #17988351C22semidirect
58. #17988348C22semidirect
59. #17988347C22semidirect
60. #17988341C22semidirect
61. #17988341C22semidirect
63. C2×#108×C73C22semidirect
65. C2×#104×C73C22semidirect
67. #408×C73C22semidirect
68. C2×C4×C8×C73C22semidirect
86. C2×#11924018C2×C4semidirect
87. C2×#11924016C2×C4semidirect
88. C2×#11924015C2×C4semidirect
89. C2×#11924013C2×C4semidirect
126. #14556519D4semidirect
130. #14556516C2×C4semidirect
131. #14556516C2×C4semidirect
132. #14556515C2×C4semidirect
133. #14556515C2×C4semidirect
134. #14556513C2×C4semidirect
135. #14556513C2×C4semidirect
136. #14556512C2×C4semidirect
137. #14556512C2×C4semidirect
157. C2×Q16×C73C2×C4semidirect
158. C2×SD16×C73C2×C4semidirect
159. C2×SD16×C73C2×C4semidirect
160. C2×D8×C73C2×C4semidirect
409. C2×D73#443semidirect
439. #1974D73semidirect
449. C73#22888semidirect
473. C2×#108C2×D73semidirect
481. C2×#104C2×D73semidirect
488. #408C2×D73semidirect
496. C2×C4×C8C2×D73semidirect
525. C2×Q16C4×D73semidirect
528. C2×SD16C4×D73semidirect
529. C2×SD16C4×D73semidirect
531. C2×D8C4×D73semidirect

Maximal subgroups

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

subgroupindex
#226191452
C2×#179887012
#226186612
C2×#104×D732
#226183792
#226106322
#226105762
#226103712
#226102612
#226102602
#226102032
#226101342
#226097682
C4×#145565032
C73×#19742
#2288873