Finite Group Databasebeta

← #33106745

Subgroups — #33106745

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
2#22618653C211yesmaximal, characteristic, complemented
3C2×#104×D73C211yesmaximal, characteristic, complemented
4#22618378C211yesmaximal, characteristic, complemented
5#22610816C211yesmaximal, characteristic, complemented
6#22610635C211yesmaximal, characteristic, complemented
7#22610578C211yesmaximal, characteristic, complemented
8#22610371C211yesmaximal, characteristic, complemented
9#22610260C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610134C211yesmaximal, characteristic, complemented
13#22609769C211yesmaximal, characteristic, complemented
14C4×#14556503C211yesmaximal, characteristic, complemented
15C2×#443×C73C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19C2×M16×D73C2211yescharacteristic
20#17989094C2211yescharacteristic
21C2×C42×D73C2211yescharacteristic
22#17988748C411yescharacteristic, complemented
23#17988746C411yescharacteristic, complemented
24#17988741C411yescharacteristic, complemented
25#17988736C411yescharacteristic, complemented
26#17988731C411yescharacteristic, complemented
27#17988729C411yescharacteristic, complemented
28#17988724C411yescharacteristic, complemented
29#17988719C411yescharacteristic, complemented
30#17988663—21no—
31#17988658—21no—
32#17988656—21no—
33C8×C22⋊D73—21no—
34C2×#14556526C2211yescharacteristic, complemented
35#17988613C2211yescharacteristic, complemented
36C2×#14556519C2211yescharacteristic
37C2×#14556518C2211yescharacteristic
38C2×#14556518C2211yescharacteristic, complemented
39C2×#14556517C2211yescharacteristic
40#104×D73—24no—
41#17988584C2211yescharacteristic
42#17988583C2211yescharacteristic
43#17988555—21no—
44#17988555C2211yescharacteristic
45#17988554C2211yescharacteristic, complemented
46#17988553—21no—
47#17988553C2211yescharacteristic
48#17988550—21no—
49#17988550C2211yescharacteristic
50C2×#14556503—21no—
51C2×#14556503C2211yescharacteristic
52C2×#14556503C2211yescharacteristic
53#17988545C2211yescharacteristic, complemented
54C2×C4×#10596831C2211yescharacteristic, complemented
55#17988352C2211yescharacteristic, complemented
56#17988351C2211yescharacteristic, complemented
57#17988348C2211yescharacteristic, complemented
58#17988347C2211yescharacteristic, complemented
59#17988341C2211yescharacteristic, complemented
60#17988341C2211yescharacteristic, complemented
61C2×#135×C73C2211yescharacteristic
62C2×#131×C73C2211yescharacteristic
63C2×#131×C73C2211yescharacteristic, complemented
64#443×C73—24no—
65C2×#108×C73C2211yescharacteristic, complemented
66C2×#104×C73C2211yescharacteristic
67C2×#104×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—41no—
85#14556611—41no—
86C2×#11924018C2×C411yescharacteristic, complemented
87C2×#11924016C2×C411yescharacteristic, complemented
88C2×#11924015C2×C411yescharacteristic, complemented
89C2×#11924013C2×C411yescharacteristic, complemented
90#14556598—22no—
91#14556598—41no—
92C2×#11924012—21no—
93C2×#11924012C2311yescharacteristic
94C2×#11924012C2311yescharacteristic
95C2×#11924011—21no—
96M16×D73—22no—
97M16×D73—41no—
98C22×#10596831—21no—
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2311yescharacteristic
101C2×C8×D73—21no—
102#14556572—21no—
103#14556567C2×C411yescharacteristic
104#14556567C2×C411yescharacteristic
105#14556562C2×C411yescharacteristic
106#14556562C2×C411yescharacteristic
107#14556559—21no—
108C4×C22⋊D73—21no—
109C4×C22⋊D73—21no—
110#14556550C2311yescharacteristic
111C2×C4×Dic73—21no—
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—22no—
114C42×D73—41no—
115#14556526—41no—
116#14556520—21no—
117#14556520—21no—
118#14556519—22no—
119#14556518—22no—
120#14556518—41no—
121#14556517—22no—
122#14556516C2×C411yescharacteristic, complemented
123#14556516C2×C411yescharacteristic, complemented
124#14556515C2×C411yescharacteristic, complemented
125#14556515C2×C411yescharacteristic, complemented
126#14556513C2×C411yescharacteristic, complemented
127#14556513C2×C411yescharacteristic, complemented
128#14556512C2×C411yescharacteristic, complemented
129#14556512C2×C411yescharacteristic, complemented
130C22⋊#10596831—21no—
131C22⋊#10596831—21no—
132#14556503—21no—
133#14556503—21no—
134#14556503—21no—
135#14556503—21no—
136#14556503—21no—
137#14556503—21no—
138#14556503C2×C411yescharacteristic
139#14556503C2×C411yescharacteristic
140#14556503C2×C411yescharacteristic
141#14556503C2×C411yescharacteristic
142#14556503D411yescharacteristic
143#14556503D411yescharacteristic
144#14556503D411yescharacteristic
145#14556503D411yescharacteristic
146#14556501—21no—
147C4×#10596831—41no—
148C8×Dic73—21no—
149C2×#41×C73C2311yescharacteristic
150C2×#41×C73C2311yescharacteristic
151#135×C73—22no—
152#135×C73—22no—
153C2×Q16×C73C2×C411yescharacteristic, complemented
154C2×SD16×C73C2×C411yescharacteristic, complemented
155C2×SD16×C73C2×C411yescharacteristic, complemented
156C2×D8×C73C2×C411yescharacteristic, complemented
157#131×C73—22no—
158#131×C73—22no—
159#131×C73—41no—
160#131×C73—41no—
161C2×M16×C73—21no—
162C2×M16×C73—21no—
163C2×M16×C73C2311yescharacteristic
164C2×M16×C73C2311yescharacteristic
165C22×C8×C73—21no—
166C22×C8×C73—21no—
167C22×C8×C73C2311yescharacteristic
168C22×C8×C73C2311yescharacteristic
169C2×C42×C73C2311yescharacteristic
170#108×C73—22no—
171#104×C73—22no—
172#104×C73D414yescomplemented
173C4×C8×C73—22no—
174C23×D73—21no—
175C23×D73#4111yescharacteristic
176#11924029—22no—
177#11924029—41no—
178#11924028—21no—
179#11924028—21no—
180#11924028—21no—
181#11924028—21no—
182#11924028—42no—
183#11924028—42no—
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—24no—
211C2×C4×D73—21no—
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—41no—
223#11924016—41no—
224#11924015—41no—
225#11924013—41no—
226#11924012—21no—
227#11924012—21no—
228#11924012—21no—
229#11924012—21no—
230#11924012—42no—
231#11924011—42no—
232C2×#10596831—21no—
233C2×#10596831—21no—
234C2×#10596831—21no—
235C2×#10596831—21no—
236C2×#10596831—21no—
237C2×#10596831—21no—
238C2×#10596831—42no—
239C2×#10596831C22×C411yescharacteristic
240C2×#10596831C22×C411yescharacteristic
241C2×#10596831C2×D411yescharacteristic
242C2×#10596831C2×D411yescharacteristic
243C8×D73—42no—
244C4⋊Dic73C22×C411yescharacteristic
245C4⋊Dic73C22×C411yescharacteristic
246#11924007—21no—
247#11924007—21no—
248C22⋊Dic73—21no—
249C22⋊Dic73—21no—
250C22⋊Dic73—21no—
251#11924005—21no—
252#11924005—21no—
253C4×Dic73—21no—
254C4×Dic73—21no—
255C4×Dic73—21no—
256C4×Dic73—42no—
257#41×C73—21no—
258#41×C73—21no—
259#41×C73—21no—
260#41×C73—21no—
261#41×C73—21no—
262#41×C73—21no—
263#41×C73C2×D412yes—
264#41×C73#4112yes—
265C2×Q8×C73C22×C411yescharacteristic
266C2×Q8×C73C22×C411yescharacteristic
267C2×D4×C73—21no—
268C2×D4×C73—21no—
269C2×D4×C73C22×C411yescharacteristic
270C2×D4×C73C22×C411yescharacteristic
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—21no—
274C22×C4×C73C2411yescharacteristic
275Q16×C73—22no—
276SD16×C73—22no—
277SD16×C73—22no—
278D8×C73—22no—
279M16×C73—21no—
280M16×C73—21no—
281M16×C73—21no—
282M16×C73—42no—
283M16×C73—42no—
284M16×C73C2×D412yes—
285C2×C8×C73—21no—
286C2×C8×C73—21no—
287C2×C8×C73—21no—
288C2×C8×C73—21no—
289C2×C8×C73—21no—
290C2×C8×C73—21no—
291C2×C8×C73—42no—
292C2×C8×C73—42no—
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—22no—
305C22×D73—21no—
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×C73C4×D412yes—
316D4×C73—22no—
317D4×C73—22no—
318D4×C73—21no—
319D4×C73—21no—
320D4×C73—21no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73C4×D412yes—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—21no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—21no—
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—42no—
340C22⋊D73—42no—
341C22⋊D73—41no—
342C22⋊D73—41no—
343C22⋊D73—42no—
344C22⋊D73—81no—
345C2×Dic73—21no—
346C2×Dic73—21no—
347C2×Dic73—22no—
348C2×Dic73—21no—
349C2×Dic73—21no—
350C2×Dic73—21no—
351C2×Dic73—42no—
352C2×Dic73—41no—
353C2×Dic73—41no—
354C2×Dic73C4×D411yescharacteristic
355C2×Dic73C4×D411yescharacteristic
356D292—21no—
357D292—21no—
358D292—42no—
359C4×D73—21no—
360C4×D73—21no—
361C4×D73—21no—
362C4×D73—21no—
363C4×D73—21no—
364C4×D73—21no—
365C4×D73—21no—
366C4×D73—21no—
367C4×D73—42no—
368C4×D73—42no—
369C4×D73—48no—
370C4×D73—41no—
371C4×D73—41no—
372Dic146—21no—
373Dic146—21no—
374Dic146—42no—
375C8×C73—21no—
376C8×C73—21no—
377C8×C73—21no—
378C8×C73—21no—
379C8×C73—22no—
380C8×C73—41no—
381#10596831—21no—
382#10596831—21no—
383#10596831—21no—
384#10596831—21no—
385#10596831—41no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—22no—
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—21no—
402C2×D73—21no—
403C2×D73—42no—
404C2×D73—42no—
405C2×D73—41no—
406C2×D73—41no—
407C2×D73—41no—
408C2×D73—84no—
409C2×D73#44312yescomplemented
410C4×C73—24no—
411C4×C73—22no—
412C4×C73—41no—
413C4×C73C2×C4×D411yescharacteristic
414C4×C73#51811yescharacteristic
415C4×C73D4211yescharacteristic
416C4×C73#54611yescharacteristic
417Dic73—21no—
418Dic73—21no—
419Dic73—42no—
420Dic73—41no—
421Dic73—41no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—21no—
426C2×C73—42no—
427C2×C73—81no—
428C2×C73#235811yescharacteristic
429C2×C73C2×#44311yescharacteristic
430C2×C73#295611yescharacteristic
431D73—22no—
432D73—41no—
433D73—81no—
434#3002—731no—
435C2×#443D7311yescharacteristic, complemented
436#2933—731no—
437C22×#104—731no—
438#2880—731no—
439#1974—731no—
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×#131C2×D7311yescharacteristic
455C2×#131C2×D7311yescharacteristic, complemented
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—24no—
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—731no—
486#408—731no—
487#408—1461no—
488#408—1461no—
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—22no—
521#135—22no—
522#135—2921no—
523#135—2921no—
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—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—2921no—
537#131—1462no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—2921no—
541C2×M16—731no—
542C2×M16—731no—
543C2×M16—1461no—
544C2×M16—1462no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—731no—
551C22×C8—731no—
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—22no—
571#108—2921no—
572C4⋊C8—1461no—
573C4⋊C8—1461no—
574#104—22no—
575#104—2921no—
576#104—1462no—
577#104—1462no—
578#104—1462no—
579#104C22⋊D7314yescomplemented
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—731no—
589C22⋊C8—731no—
590C22⋊C8—731no—
591C22⋊C8—731no—
592C22⋊C8—731no—
593C22⋊C8—731no—
594C22⋊C8—731no—
595C22⋊C8—731no—
596C22⋊C8—1461no—
597C22⋊C8—1461no—
598C22⋊C8—1461no—
599C22⋊C8—1461no—
600C22⋊C8—1461no—
601C22⋊C8—1461no—
602C22⋊C8—1461no—
603C22⋊C8—1461no—
604#97—1461no—
605C4×C8—22no—
606C4×C8—2921no—
607C4×C8—1461no—
608C24—731no—
609C24—1461no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—2922no—
617#41—2922no—
618#41—2922no—
619#41—2922no—
620#41—2921no—
621#41—2921no—
622#41—1462no—
623#41—1462no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627#41—1461no—
628#41C2×C22⋊D7312yes—
629#41#1192402812yes—
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—1461no—
645C2×D4—1461no—
646C2×D4—1461no—
647C2×D4—1462no—
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—22no—
675Q16—2921no—
676SD16—22no—
677SD16—22no—
678SD16—2921no—
679SD16—2921no—
680D8—22no—
681D8—2921no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—2922no—
688M16—2922no—
689M16—1461no—
690M16—1461no—
691M16—1461no—
692M16—1461no—
693M16C2×C22⋊D7312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
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—
732C42C2×C22⋊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—2922no—
750Q8—1461no—
751Q8—1461no—
752Q8C4×C22⋊D7312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—41no—
759D4—41no—
760D4—2922no—
761D4—2922no—
762D4—2922no—
763D4—2921no—
764D4—2921no—
765D4—2922no—
766D4—5841no—
767D4—1461no—
768D4—1461no—
769D4C4×C22⋊D7312yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
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—2921no—
786C2×C4—2921no—
787C2×C4—731no—
788C2×C4—731no—
789C2×C4—1462no—
790C2×C4—1461no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1461no—
795C2×C4—1461no—
796C2×C4—1461no—
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×C4C22×C22⋊D7311yescharacteristic
806C2×C4C2×#1192402811yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663711yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—2921no—
816C8—2921no—
817C8—1461no—
818C8—1461no—
819C8—1461no—
820C8—1461no—
821C22—21no—
822C22—21no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—2922no—
830C22—2922no—
831C22—2921no—
832C22—2921no—
833C22—2921no—
834C22—5844no—
835C22—732no—
836C22—1461no—
837C22—1461no—
838C22—1461no—
839C22—1461no—
840C22—1461no—
841C22C4×D4×D7311yescharacteristic
842C22#1798922511yescharacteristic
843C22#1798926611yescharacteristic
844C4—24no—
845C4—22no—
846C4—41no—
847C4—2922no—
848C4—2921no—
849C4—2921no—
850C4—2921no—
851C4—1461no—
852C4—1461no—
853C4C2×C4×C22⋊D7311yescharacteristic
854C4#1798905911yescharacteristic
855C4D4×C22⋊D7311yescharacteristic
856C4#1798923311yescharacteristic
857C2—21no—
858C2—21no—
859C2—42no—
860C2—81no—
861C2—2921no—
862C2—5841no—
863C2—1462no—
864C2#2261290811yescharacteristic
865C2#443×D7311yescharacteristic
866C2#2261883611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×#443×C73C2
socleC22×C73C2×C4×D4
prime radical#22619145C2
cosocleC22×C4×C73C24
hypercenterC2×#443D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. #22618653C2semidirect
3. C2×#104×D73C2semidirect
4. #22618378C2semidirect
5. #22610816C2semidirect
6. #22610635C2semidirect
7. #22610578C2semidirect
8. #22610371C2semidirect
9. #22610260C2semidirect
10. #22610258C2semidirect
11. #22610206C2semidirect
12. #22610134C2semidirect
13. #22609769C2semidirect
14. C4×#14556503C2semidirect
15. C2×#443×C73C2semidirect
22. #17988748C4semidirect
23. #17988746C4semidirect
24. #17988741C4semidirect
25. #17988736C4semidirect
26. #17988731C4semidirect
27. #17988729C4semidirect
28. #17988724C4semidirect
29. #17988719C4semidirect
34. C2×#14556526C22semidirect
35. #17988613C22semidirect
38. C2×#14556518C22semidirect
45. #17988554C22semidirect
53. #17988545C22semidirect
54. C2×C4×#10596831C22semidirect
55. #17988352C22semidirect
56. #17988351C22semidirect
57. #17988348C22semidirect
58. #17988347C22semidirect
59. #17988341C22semidirect
60. #17988341C22semidirect
63. C2×#131×C73C22semidirect
65. C2×#108×C73C22semidirect
67. C2×#104×C73C22semidirect
68. C2×C4×C8×C73C22semidirect
86. C2×#11924018C2×C4semidirect
87. C2×#11924016C2×C4semidirect
88. C2×#11924015C2×C4semidirect
89. C2×#11924013C2×C4semidirect
122. #14556516C2×C4semidirect
123. #14556516C2×C4semidirect
124. #14556515C2×C4semidirect
125. #14556515C2×C4semidirect
126. #14556513C2×C4semidirect
127. #14556513C2×C4semidirect
128. #14556512C2×C4semidirect
129. #14556512C2×C4semidirect
153. C2×Q16×C73C2×C4semidirect
154. C2×SD16×C73C2×C4semidirect
155. C2×SD16×C73C2×C4semidirect
156. C2×D8×C73C2×C4semidirect
172. #104×C73D4semidirect
409. C2×D73#443semidirect
435. C2×#443D73semidirect
449. C73#22888semidirect
455. C2×#131C2×D73semidirect
473. C2×#108C2×D73semidirect
481. C2×#104C2×D73semidirect
496. C2×C4×C8C2×D73semidirect
525. C2×Q16C4×D73semidirect
528. C2×SD16C4×D73semidirect
529. C2×SD16C4×D73semidirect
531. C2×D8C4×D73semidirect
579. #104C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226191452
#226186532
C2×#104×D732
#226183782
#226108162
#226106352
#226105782
#226103712
#226102602
#226102582
#226102062
#226101342
#226097692
C4×#145565032
C2×#443×C732
#2288873