Finite Group Databasebeta

← #29700751

Subgroups — #29700751

Order 15616.

1058 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#21455035C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3C22×#14519703C211yesmaximal, characteristic, complemented
4#21454265C211yesmaximal, characteristic, complemented
5#21446711C211yesmaximal, characteristic, complemented
6#21446529C211yesmaximal, characteristic, complemented
7#21446467C211yesmaximal, characteristic, complemented
8#21446263C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446146C211yesmaximal, characteristic, complemented
11#21446093C211yesmaximal, characteristic, complemented
12#21446024C211yesmaximal, characteristic, complemented
13#21445665C211yesmaximal, characteristic, complemented
14#21445583C211yesmaximal, characteristic, complemented
15C61×#2933C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519783C2211yescharacteristic
20C2×#14519783C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839922C411yescharacteristic, complemented
23#16839922C411yescharacteristic, complemented
24#16839917C411yescharacteristic, complemented
25#16839912C411yescharacteristic, complemented
26#16839905C411yescharacteristic, complemented
27#16839905C411yescharacteristic, complemented
28#16839900C411yescharacteristic, complemented
29#16839895C411yescharacteristic, complemented
30#16839882—24no—
31C2×#14519712C2211yescharacteristic, complemented
32C2×#14519712C2211yescharacteristic, complemented
33C2×#14519704C2211yescharacteristic, complemented
34C2×#14519704C2211yescharacteristic, complemented
35C2×#14519703—24no—
36C2×#14519703C2211yescharacteristic
37C2×#14519703C2211yescharacteristic
38C2×#14519703C2211yescharacteristic
39C2×#14519703C2211yescharacteristic
40#16839756C2211yescharacteristic
41#16839756C2211yescharacteristic
42#16839728C2211yescharacteristic
43#16839728C2211yescharacteristic
44#16839727—21no—
45#16839727—21no—
46#16839726C2211yescharacteristic
47#16839724—21no—
48C2×C22⋊#92418C2211yescharacteristic
49C22⋊C8×D61—21no—
50C2×#14519687C2211yescharacteristic, complemented
51C2×#14519687C2211yescharacteristic, complemented
52#16839526C2211yescharacteristic, complemented
53#16839526C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56#16839516C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58C2×#131×C61C2211yescharacteristic, complemented
59C22×M16×C61C2211yescharacteristic
60C61×#525C2211yescharacteristic
61C61×#436—21no—
62C61×#435—21no—
63C61×#435—21no—
64C8×D4×C61—21no—
65C61×#424C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C61C2211yescharacteristic
68C61×#405C2211yescharacteristic, complemented
69C2×#11758222—21no—
70C2×#11758222—21no—
71C2×#11758222—22no—
72C2×#11758222—22no—
73C2×#11758222—41no—
74C2×#11758222—41no—
75C2×#11758222C2×C411yescharacteristic
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222C2311yescharacteristic
78C2×#11758222C2311yescharacteristic
79C22×Dic122C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C22×C22⋊D61—21no—
82C23×Dic61—21no—
83C22×C4×D61—21no—
84#14519797—22no—
85#14519797—22no—
86#14519797—41no—
87#14519797—41no—
88C2×#11758202C2×C411yescharacteristic, complemented
89C2×#11758202C2×C411yescharacteristic, complemented
90C2×#11758200C2×C411yescharacteristic, complemented
91C2×#11758200C2×C411yescharacteristic, complemented
92C2×#11758201C2×C411yescharacteristic, complemented
93C2×#11758201C2×C411yescharacteristic, complemented
94C2×#11758199C2×C411yescharacteristic, complemented
95C2×#11758199C2×C411yescharacteristic, complemented
96#14519783—22no—
97#14519783—22no—
98#14519783—41no—
99#14519783—41no—
100C2×#11758194C2311yescharacteristic
101C2×#11758194C2311yescharacteristic
102C2×#11758189—21no—
103C2×#11758189—21no—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C2×C8×D61—21no—
107C2×C8×D61—21no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—41no—
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113#14519712—22no—
114#14519712—41no—
115#14519704—22no—
116#14519704—41no—
117#14519703—22no—
118#14519703—22no—
119#14519703—22no—
120#14519703D414yescomplemented
121#14519700C2×C411yescharacteristic, complemented
122#14519700C2×C411yescharacteristic, complemented
123#14519700C2×C411yescharacteristic, complemented
124#14519700C2×C411yescharacteristic, complemented
125#14519697C2×C411yescharacteristic, complemented
126#14519697C2×C411yescharacteristic, complemented
127#14519697C2×C411yescharacteristic, complemented
128#14519697C2×C411yescharacteristic, complemented
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131C22⋊#92418C2×C411yescharacteristic
132C22⋊#92418C2×C411yescharacteristic
133C22⋊#92418C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—21no—
139#14519687—22no—
140#14519687—41no—
141C2×#41×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143#131×C61—22no—
144#131×C61—41no—
145C2×M16×C61—21no—
146C2×M16×C61—21no—
147C2×M16×C61—22no—
148C2×M16×C61—41no—
149C2×M16×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C22×C8×C61—21no—
152C22×C8×C61—21no—
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155#123×C61—21no—
156C22⋊Q8×C61C2×C411yescharacteristic
157C22⋊Q8×C61C2×C411yescharacteristic
158#121×C61C2×C411yescharacteristic
159#121×C61C2×C411yescharacteristic
160#120×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163#117×C61C2311yescharacteristic
164C4⋊C8×C61—21no—
165C4⋊C8×C61—21no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172#97×C61—21no—
173C4×C8×C61—21no—
174C24×C61#4111yescharacteristic
175C23×D61—21no—
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61—42no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61—42no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—21no—
212#11758222—21no—
213#11758222—21no—
214#11758222—22no—
215#11758222—22no—
216#11758222—41no—
217#11758222—41no—
218#11758222—42no—
219#11758222—42no—
220#11758222—42no—
221#11758222—42no—
222#11758222C2×D412yes—
223#11758222#4112yes—
224C2×D244—22no—
225C2×D244—21no—
226C2×D244—41no—
227C2×D244C22×C411yescharacteristic
228C2×D244C22×C411yescharacteristic
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×Dic122—22no—
236C2×Dic122—21no—
237C2×Dic122—41no—
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—42no—
244M16×C61—42no—
245M16×C61C2×D412yes—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—42no—
253C2×C8×C61—42no—
254C2×C8×C61C2×D411yescharacteristic
255C2×C8×C61C2×D411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C2×C8×C61C2×D411yescharacteristic
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C42×C61—21no—
268#11758202—22no—
269#11758202—41no—
270#11758201—22no—
271#11758201—41no—
272#11758200—22no—
273#11758200—41no—
274#11758199—22no—
275#11758199—41no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61—42no—
280C4×Dic61C2×D412yes—
281#11758194—21no—
282#11758194—21no—
283#11758194—21no—
284#11758194—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418C22×C411yescharacteristic
292C2×#92418C22×C411yescharacteristic
293C2×#92418C22×C411yescharacteristic
294C2×#92418C22×C411yescharacteristic
295#11758189—42no—
296#11758189—42no—
297C8×D61—42no—
298C8×D61—42no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—41no—
304C23×C61C4×D411yescharacteristic
305C23×C61C4×D411yescharacteristic
306C23×C61C2×#4111yescharacteristic
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—42no—
310C22×D61—42no—
311C22×D61—81no—
312Q8×C61—21no—
313Q8×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—42no—
319D4×C61—81no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61C4×D411yescharacteristic
336C2×C4×C61C4×D411yescharacteristic
337C2×C4×C61C23×C411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C22⋊D61—22no—
344C22⋊D61—22no—
345C22⋊D61—42no—
346C22⋊D61—42no—
347C22⋊D61—41no—
348C22⋊D61—41no—
349C2×Dic61—21no—
350C2×Dic61—22no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—42no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—48no—
358C2×Dic61—41no—
359D244—21no—
360D244—21no—
361D244—21no—
362D244—42no—
363D244C4×D412yes—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—41no—
369C4×D61—41no—
370Dic122—21no—
371Dic122—21no—
372Dic122—21no—
373Dic122—42no—
374Dic122C4×D412yes—
375C8×C61—21no—
376C8×C61—21no—
377C8×C61—22no—
378C8×C61—21no—
379C8×C61—21no—
380C8×C61—41no—
381#92418—21no—
382#92418—21no—
383#92418—21no—
384#92418—21no—
385#92418—41no—
386#92418—41no—
387#22886—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61#44412yescomplemented
401C22×C61C2×C4×D411yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61#55111yescharacteristic
404C2×D61—22no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—84no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—41no—
416C4×C61C2×C4×D411yescharacteristic
417C4×C61#51811yescharacteristic
418C4×C61D4211yescharacteristic
419C4×C61#54611yescharacteristic
420Dic61—22no—
421Dic61—42no—
422Dic61—42no—
423Dic61—41no—
424#3002—611no—
425C2×#444—611no—
426#2933D6111yescharacteristic, complemented
427C22×#104—611no—
428#2880—611no—
429#1975—611no—
430#1938—611no—
431#1929—611no—
432#1896—611no—
433#1876—611no—
434#1876—611no—
435#1866—611no—
436#1855—611no—
437#1765—611no—
438#1749—611no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—21no—
442C2×C61—41no—
443C2×C61—81no—
444C2×C61#235811yescharacteristic
445C2×C61C2×#44411yescharacteristic
446C2×C61#295611yescharacteristic
447D61—42no—
448D61—81no—
449C22×#41—611no—
450C2×#135—611no—
451C2×#135—611no—
452C2×#131—611no—
453C2×#131—611no—
454C2×#131C2×D6111yescharacteristic, complemented
455C22×M16C2×D6111yescharacteristic
456#525C2×D6111yescharacteristic
457C22×C42—611no—
458#452—611no—
459#452—611no—
460#451—611no—
461#450—611no—
462#449—611no—
463#449—611no—
464#448—611no—
465#447—611no—
466#444—1224no—
467#436—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108—611no—
472C2×#108—611no—
473#424C2×D6111yescharacteristic, complemented
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478C2×#104—611no—
479C2×#104—611no—
480C2×#104—1224no—
481#416—611no—
482#416—611no—
483#408—611no—
484#408—611no—
485#408—1221no—
486#408—1221no—
487#408C2×D6111yescharacteristic, complemented
488#407—611no—
489#407—1221no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—1221no—
492C2×C22⋊C8C2×D6111yescharacteristic
493#405C2×D6111yescharacteristic, complemented
494C2×#97—611no—
495C2×#97—611no—
496#341—611no—
497#341—611no—
498#339—611no—
499#339—611no—
500#336—611no—
501#336—611no—
502C61#2288611yescharacteristic, complemented, Sylow
503C2×#41—611no—
504C2×#41—611no—
505C2×#41—611no—
506C2×#41—611no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—1221no—
510C2×#41—1221no—
511C2×#41—2441no—
512C2×#41—2441no—
513C2×#41C22×D6111yescharacteristic
514C22×Q8—611no—
515C22×D4—611no—
516C22×D4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C23×C4C22×D6111yescharacteristic
520#135—1222no—
521#135—1222no—
522#135—2441no—
523#135—2441no—
524C2×Q16—611no—
525C2×Q16—611no—
526C2×SD16—611no—
527C2×SD16—611no—
528C2×SD16—611no—
529C2×SD16—611no—
530C2×D8—611no—
531C2×D8—611no—
532#131—22no—
533#131—41no—
534#131—1222no—
535#131—1222no—
536#131—2441no—
537#131—2441no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—611no—
543C2×M16—611no—
544C2×M16—1221no—
545C2×M16—1221no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—611no—
551C22×C8—611no—
552C22×C8—1221no—
553C22×C8—1221no—
554C22×C8C22×D6111yescharacteristic
555C22×C8C22×D6111yescharacteristic
556#123—21no—
557C22⋊Q8C4×D6111yescharacteristic
558C22⋊Q8C4×D6111yescharacteristic
559#121C4×D6111yescharacteristic
560#121C4×D6111yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D6111yescharacteristic
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—1222no—
568C2×C42—1221no—
569C2×C42—2441no—
570#108—1222no—
571#108—2441no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—614no—
575#104—1222no—
576#104—1222no—
577#104—1222no—
578#104—1222no—
579#104—2441no—
580#103—611no—
581#103—611no—
582#103—611no—
583#103—611no—
584#102—611no—
585#102—611no—
586#102—611no—
587#102—611no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8C22⋊D6111yescharacteristic
601C22⋊C8C22⋊D6111yescharacteristic
602C22⋊C8C22⋊D6111yescharacteristic
603C22⋊C8C22⋊D6111yescharacteristic
604#97—21no—
605#97—1222no—
606#97—2441no—
607C4×C8—21no—
608C24—1221no—
609C24#1175822211yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—612no—
615#41—612no—
616#41—1222no—
617#41—1222no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627#41—2441no—
628#41—2442no—
629#41—2442no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—1222no—
633C2×Q8—1221no—
634C2×Q8—2441no—
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—611no—
640C2×D4—611no—
641C2×D4—1222no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—2441no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4C2×C4×D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4—2442no—
668C22×C4C2×C4×D6111yescharacteristic
669C22×C4C2×C4×D6111yescharacteristic
670C22×C4#1175822211yescharacteristic
671C22×C4C2×C22⋊D6111yescharacteristic
672C22×C4C2×C22⋊D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674Q16—1222no—
675Q16—2441no—
676SD16—1222no—
677SD16—1222no—
678SD16—2441no—
679SD16—2441no—
680D8—1222no—
681D8—2441no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—2442no—
692M16—2442no—
693M16D4×D6112yes—
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—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—611no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—2442no—
713C2×C8—2442no—
714C2×C8C2×C22⋊D6111yescharacteristic
715C2×C8C2×C22⋊D6111yescharacteristic
716C2×C8C2×C22⋊D6111yescharacteristic
717C2×C8C2×C22⋊D6111yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D6111yescharacteristic
721C4⋊C4C2×C4×D6111yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—612no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—2442no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—1221no—
739C23—1221no—
740C23—4881no—
741C23—2442no—
742C23—2442no—
743C23C4×C22⋊D6111yescharacteristic
744C23C4×C22⋊D6111yescharacteristic
745C23C2×#1175822211yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—612no—
749Q8—1221no—
750Q8—1221no—
751Q8—1221no—
752Q8—2442no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—612no—
760D4—1222no—
761D4—1222no—
762D4—1221no—
763D4—1221no—
764D4—1221no—
765D4—2442no—
766D4—2442no—
767D4—2442no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—1221no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2448no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4C4×C22⋊D6111yescharacteristic
802C2×C4C4×C22⋊D6111yescharacteristic
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4#41×D6111yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—1221no—
816C8—1221no—
817C8—1221no—
818C8—1221no—
819C8—2441no—
820C8—2441no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—1222no—
834C22—4884no—
835C22—2441no—
836C22—2441no—
837C22—2441no—
838C22—2441no—
839C22—2441no—
840C22#1683988212yescomplemented
841C22C2×C4×C22⋊D6111yescharacteristic
842C22#1684040811yescharacteristic
843C22#1684044111yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—1222no—
850C4—2442no—
851C4—2442no—
852C4—2441no—
853C4C4×D4×D6111yescharacteristic
854C4#1684023411yescharacteristic
855C4D4×C22⋊D6111yescharacteristic
856C4#1684040011yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4881no—
863C2—2442no—
864C2#2144879611yescharacteristic
865C2C2×#1683988211yescharacteristic
866C2#2145472611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2933C2
socleC22×C61C2×C4×D4
prime radical#21455035C2
cosocleC22×C4×C61C24
hypercenter#2933D61
hypocenterC61#22886
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. C22×#14519703C2semidirect
4. #21454265C2semidirect
5. #21446711C2semidirect
6. #21446529C2semidirect
7. #21446467C2semidirect
8. #21446263C2semidirect
9. #21446149C2semidirect
10. #21446146C2semidirect
11. #21446093C2semidirect
12. #21446024C2semidirect
13. #21445665C2semidirect
14. #21445583C2semidirect
15. C61×#2933C2semidirect
22. #16839922C4semidirect
23. #16839922C4semidirect
24. #16839917C4semidirect
25. #16839912C4semidirect
26. #16839905C4semidirect
27. #16839905C4semidirect
28. #16839900C4semidirect
29. #16839895C4semidirect
31. C2×#14519712C22semidirect
32. C2×#14519712C22semidirect
33. C2×#14519704C22semidirect
34. C2×#14519704C22semidirect
50. C2×#14519687C22semidirect
51. C2×#14519687C22semidirect
52. #16839526C22semidirect
53. #16839526C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
56. #16839516C22semidirect
57. #16839516C22semidirect
58. C2×#131×C61C22semidirect
65. C61×#424C22semidirect
66. C61×#408C22semidirect
68. C61×#405C22semidirect
88. C2×#11758202C2×C4semidirect
89. C2×#11758202C2×C4semidirect
90. C2×#11758200C2×C4semidirect
91. C2×#11758200C2×C4semidirect
92. C2×#11758201C2×C4semidirect
93. C2×#11758201C2×C4semidirect
94. C2×#11758199C2×C4semidirect
95. C2×#11758199C2×C4semidirect
120. #14519703D4semidirect
121. #14519700C2×C4semidirect
122. #14519700C2×C4semidirect
123. #14519700C2×C4semidirect
124. #14519700C2×C4semidirect
125. #14519697C2×C4semidirect
126. #14519697C2×C4semidirect
127. #14519697C2×C4semidirect
128. #14519697C2×C4semidirect
400. C22×C61#444semidirect
426. #2933D61semidirect
454. C2×#131C2×D61semidirect
473. #424C2×D61semidirect
487. #408C2×D61semidirect
493. #405C2×D61semidirect
502. C61#22886semidirect
840. C22#16839882semidirect

Maximal subgroups

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

subgroupindex
#214550352
C2×#168398822
C22×#145197032
#214542652
#214467112
#214465292
#214464672
#214462632
#214461492
#214461462
#214460932
#214460242
#214456652
#214455832
C61×#29332
#2288661