Finite Group Databasebeta

← #72222817

Subgroups — #72222817

Order 2304.

1368 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11899653C211yesmaximal, characteristic
2C3×#79249C211yesmaximal, characteristic, complemented
3#11860967C211yesmaximal, characteristic, complemented
4#11797981C214yesmaximal, complemented
5#11797935C214yesmaximal, complemented
6C2×#10589360C211yesmaximal, characteristic, complemented
7C3×#70687C211yesmaximal, characteristic, complemented
8C2×#10589124C211yesmaximal, characteristic, complemented
9#11795946C211yesmaximal, characteristic, complemented
10#10948649—31nomaximal
11#10948646—31nomaximal
12C3×#5745—21no—
13C2×C3×#904C2211yescharacteristic
14C2×C3×#904C2211yescharacteristic
15#10594992—21no—
16C2×C32×#108C2211yescharacteristic
17C2×#63644C2211yescharacteristic
18C2×#63639C2211yescharacteristic
19C3×#5139—21no—
20C3×#5101C2211yescharacteristic
21C2×C3×#812C2211yescharacteristic
22C3×#4895—22no—
23C3×#4894C2214yes—
24#10591088—21no—
25#10590812C2212yescomplemented
26#10590771C2212yescomplemented
27Dic3×#204—22no—
28#10590636C412yescomplemented
29#10590636C2212yes—
30#10590630C412yescomplemented
31#10590630C2212yes—
32#10590629C414yescomplemented
33#10589360C2214yescomplemented
34C3×#4496C2212yescomplemented
35C3×#4495C2212yescomplemented
36#10589124C2214yes—
37#10589105C2214yescomplemented
38C3×#2957—31no—
39#83899—31no—
40#83894—31no—
41#83894—31no—
42#79249D311yescharacteristic, complemented
43#78574—31no—
44C3×#2148—31no—
45C2×#4566—31no—
46C2×#4518—31no—
47#71425—31no—
48#70929—34no—
49#70928—34no—
50#70687D311yescharacteristic, complemented
51C2×#4494—31no—
52C2×#4494—31no—
53C2×#4494—61no—
54#69884—31no—
55#69264—34no—
56#69254—34no—
57C2×C3×#235—21no—
58C2×C3×#235—21no—
59C2×C32×M16—21no—
60C22×C32×C8C2311yescharacteristic
61C2×C4⋊(C3⋊Dic3)—21no—
62C3×#926D411yescharacteristic
63C2×C3×#208D411yescharacteristic
64C3×#907—24no—
65C3×D3×M16—42no—
66C2×C3×Dic12C2×C411yescharacteristic, complemented
67C2×C3×Dic12C2311yescharacteristic
68C3×#904—21no—
69C3×#904—21no—
70C3×#904—21no—
71C3×#904—21no—
72C3×#904C2×C412yes—
73C3×#904C2×C412yes—
74C3×#904C2×C412yescomplemented
75C3×#904C2312yes—
76C2×C3×D24C2×C411yescharacteristic, complemented
77C2×C3×D24C2311yescharacteristic
78C2×C3×#204—21no—
79C2×C3×#204—21no—
80C3×#901—42no—
81#67⋊Dic3—42no—
82Dic3×D12—22no—
83D3×C4⋊Dic3—41no—
84Dic3×Dic6—22no—
85#63841—41no—
86C32×#108—21no—
87C32×#108C2312yes—
88#63644—21no—
89#63644C2312yes—
90#63639C2×C412yescomplemented
91#63639C2312yes—
92C2×C3⋊(C3⋊C16)C2×C412yescomplemented
93C3×#825—24no—
94C3×#815C2312yes—
95C3×C8×Dic3D412yes—
96C3×#812—21no—
97C3×#812C2312yes—
98C2×C3×C3⋊C16—21no—
99#63566—22no—
100#63563—22no—
101#63550C2×C414yescomplemented
102#63547C2×C414yescomplemented
103#63547C2×C414yescomplemented
104#63545C2×C414yescomplemented
105#33469—91noSylow
106C2×C3×#135—31no—
107C2×C3×#135—31no—
108C3×#568—61no—
109#5827—61no—
110#5745—21no—
111C2×#904C2×D311yescharacteristic
112C2×#904C2×D311yescharacteristic
113#5523—61no—
114C2×C3×M32—31no—
115C3×#444—34no—
116C3×#443—62no—
117C2×C3×#108—21no—
118C2×C3×#108C2×D311yescharacteristic
119C2×C3×#108C2×D311yescharacteristic
120C3×#421—61no—
121C3×#405—31no—
122#5232—61no—
123#5195—32no—
124#5195—32no—
125#5194—34no—
126#5194—34no—
127#5193—32no—
128#5193—32no—
129#5184—32no—
130#5179—32no—
131#5179—32no—
132Dic3×SD16—62no—
133#5152—32no—
134#5147—32no—
135#5147—32no—
136#5139—21no—
137#5133—61no—
138C2×#817—31no—
139C2×#817—31no—
140C2×#817—61no—
141#5101C2×D311yescharacteristic
142C2×#812—31no—
143C2×#812—31no—
144C2×#812—61no—
145C2×#812C2×D311yescharacteristic
146#4895—22no—
147#4894C2×D314yes—
148#4716—32no—
149#4711—32no—
150C4×#204—62no—
151C3×#362—32no—
152C3×#361—32no—
153#4566—34no—
154#4518—34no—
155#4512—34no—
156#4496C2×D312yescomplemented
157#4495C2×D312yescomplemented
158#4494—34no—
159#4494—34no—
160#4494—64no—
161#4466—34no—
162C22×C32×C4C2×D411yescharacteristic
163C22×C3⋊Dic3—41no—
164C2×C3×#67—41no—
165C2×C3×#67—41no—
166C3×#235—22no—
167C3×#235—22no—
168C3×#235—22no—
169C3×#235—22no—
170C3×#235—41no—
171C3×#235—41no—
172C3×#235—41no—
173C3×#235—41no—
174C2×C3×D12—21no—
175C2×C3×D12—21no—
176C2×C3×C4×D3—41no—
177C2×C3×C4×D3—41no—
178C2×C3×Dic6—21no—
179C2×C3×Dic6—21no—
180C2×D3×Dic3—42no—
181C32×M16—22no—
182C32×M16—41no—
183C2×C32×C8—41no—
184C2×C32×C8C22×C411yescharacteristic
185C2×C32×C8C22×C411yescharacteristic
186C2×C32×C8C2×D411yescharacteristic
187C2×C32×C8#4111yescharacteristic
188C2×C32×C8#4111yescharacteristic
189C2×C32×C8C2411yescharacteristic
190C4⋊(C3⋊Dic3)—22no—
191C4⋊(C3⋊Dic3)—41no—
192C3×#217—21no—
193C3×C4⋊Dic3—21no—
194C3×C4×Dic3C2×D412yes—
195C3×#208—21no—
196C3×#208—21no—
197C2×C3×C3⋊C8C2×D412yes—
198C3×Dic12—21no—
199C3×Dic12—21no—
200C3×Dic12C22×C412yes—
201C3×Dic12C22×C412yes—
202C3×D24—21no—
203C3×D24—21no—
204C3×D24C22×C412yes—
205C3×D24C22×C412yes—
206C3×#204—22no—
207C3×#204—22no—
208C3×#204—22no—
209C3×#204—22no—
210C3×ΓL(1,𝔽25)—44no—
211C3×D3×C8—44no—
212Dic3⋊Dic3—42no—
213(C2×D3)⋊Dic3—42no—
214Dic32—42no—
215C3⋊(C3⋊C16)C22×C414yes—
216C3×C3⋊C16—22no—
217#3414—91no—
218#2957—31no—
219#2952—91no—
220AGL(1,ℤ/16)—94no—
221#2180—94no—
222C2×#365—91no—
223#2148—31no—
224C2×#360—91no—
225#2110—91no—
226C2×C3×#41—61no—
227C2×C3×#41—61no—
228C2×#235—21no—
229C2×#235—21no—
230C3×#135—32no—
231C3×#135—32no—
232C3×#135—32no—
233C3×#135—32no—
234C3×#135—61no—
235C3×#135—61no—
236C3×#135—61no—
237C3×#135—61no—
238C2×C3×Q16—31no—
239C2×C3×Q16—31no—
240C2×C3×SD16—61no—
241C2×C3×SD16—61no—
242C2×C3×D8—31no—
243C2×C3×D8—31no—
244C3×#131—64no—
245C3×#131—122no—
246C2×C3×M16—21no—
247C2×C3×M16—21no—
248C2×C3×M16—31no—
249C2×C3×M16—41no—
250C2×C3×M16—122no—
251C22×C3×C8—21no—
252C22×C3×C8C22×D311yescharacteristic
253C22×C3×C8C22×D311yescharacteristic
254C3×#117—31no—
255Q8×Dic3—62no—
256D4×Dic3—62no—
257D4×Dic3—122no—
258#926—121no—
259#926#6711yescharacteristic
260C2×C4⋊Dic3—61no—
261C2×C4⋊Dic3—61no—
262C2×C4⋊Dic3—121no—
263C2×C4⋊Dic3—121no—
264C2×#208#6711yescharacteristic
265#907—24no—
266D3×M16—42no—
267C2×Dic12C4×D311yescharacteristic, complemented
268C2×Dic12C22×D311yescharacteristic
269#904—21no—
270#904—21no—
271#904—21no—
272#904—21no—
273#904C4×D312yes—
274#904C4×D312yes—
275#904C4×D312yescomplemented
276#904C22×D312yes—
277C2×D24C4×D311yescharacteristic, complemented
278C2×D24C22×D311yescharacteristic
279C2×#204—21no—
280C2×#204—21no—
281#901—42no—
282#892—121no—
283D3×C4⋊C4—121no—
284#67⋊C4—122no—
285C4×D12—62no—
286C4×Dic6—62no—
287C3×M32—32no—
288C3×M32—61no—
289C2×C3×C16—61no—
290C3×#108—21no—
291C3×#108—21no—
292C3×#108—22no—
293C3×#108—41no—
294C3×#108C22×D312yes—
295C3×#108C22×D312yes—
296C3×#104—64no—
297C3×#97—32no—
298C3×C4×C8—32no—
299#835—62no—
300#832—62no—
301#829—34no—
302#829—34no—
303#828—34no—
304#828—34no—
305#827—34no—
306#827—34no—
307#826—34no—
308#826—34no—
309#825—24no—
310#821—62no—
311#817—32no—
312#817—32no—
313#817—62no—
314#817—61no—
315#817—61no—
316#817—121no—
317#816—62no—
318#815C22×D312yes—
319C8×Dic3#6712yes—
320#812—21no—
321#812—32no—
322#812—32no—
323#812—32no—
324#812—32no—
325#812—62no—
326#812—62no—
327#812C22×D312yes—
328C2×C3⋊C16—21no—
329C2×C3⋊C16—32no—
330C2×C3⋊C16—32no—
331C2×C3⋊C16—62no—
332C23×C32AGL(1,ℤ/8)11yescharacteristic
333C22×C3×D3—41no—
334C22×C3×D3—41no—
335C2×C32×C4C4×D411yescharacteristic
336C2×C32×C4C4×D411yescharacteristic
337C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
338C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
339C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
340C2×C32×C4C22×D411yescharacteristic
341C2×C3⋊Dic3—42no—
342C2×C3⋊Dic3—161no—
343C3×#67—42no—
344C3×#67—42no—
345C3×#67—42no—
346C3×#67—42no—
347C2×C3×Dic3—22no—
348C2×C3×Dic3—41no—
349C2×C3×Dic3—41no—
350C3×D12—22no—
351C3×D12—22no—
352C3×D12—41no—
353C3×D12—41no—
354C3×C4×D3—42no—
355C3×C4×D3—42no—
356C3×C4×D3—42no—
357C3×C4×D3—42no—
358C3×Dic6—22no—
359C3×Dic6—22no—
360C3×Dic6—41no—
361C3×Dic6—41no—
362D3×Dic3—162no—
363C32×C8—42no—
364C32×C8C4×D411yescharacteristic
365C32×C8C4×D411yescharacteristic
366C32×C8C23×C411yescharacteristic
367C32×C8C2×#4111yescharacteristic
368C3×C3⋊C8—22no—
369C2×#135—31no—
370C2×#135—31no—
371#568—61no—
372#520—181no—
373#510—92no—
374#510—92no—
375#509—92no—
376#509—92no—
377#508—94no—
378C2×M32—31no—
379C2×M32—91no—
380#444—34no—
381#443—62no—
382#442—92no—
383#441—92no—
384C4×SD16—182no—
385C2×#108D3211yescharacteristic
386C2×#106—91no—
387#421—61no—
388#417—181no—
389#405—31no—
390#365—94no—
391#362—32no—
392#361—32no—
393#360—94no—
394#347—94no—
395C3×#41—62no—
396C3×#41—62no—
397C3×#41—62no—
398C3×#41—62no—
399C3×#41—121no—
400C3×#41—121no—
401C3×#41—121no—
402C3×#41—121no—
403C2×C3×Q8—61no—
404C2×C3×Q8—61no—
405C2×C3×D4—61no—
406C2×C3×D4—61no—
407C2×C3×D4—121no—
408C2×C3×D4—121no—
409C22×C3×C4—21no—
410C22×C3×C4—121no—
411C22×C3×C4—121no—
412C22×C3×C4D3×D411yescharacteristic
413C22×C3×C4C2×#6711yescharacteristic
414C2×#67—41no—
415C2×#67—41no—
416C22×Dic3—122no—
417C22×Dic3—121no—
418C22×Dic3—121no—
419C22×Dic3—241no—
420#235—22no—
421#235—22no—
422#235—22no—
423#235—22no—
424#235—41no—
425#235—41no—
426#235—41no—
427#235—41no—
428C2×D12—21no—
429C2×D12—21no—
430C2×C4×D3—41no—
431C2×C4×D3—41no—
432C2×C4×D3—122no—
433C2×Dic6—21no—
434C2×Dic6—21no—
435C3×Q16—32no—
436C3×Q16—32no—
437C3×Q16—61no—
438C3×Q16—61no—
439C3×SD16—62no—
440C3×SD16—62no—
441C3×SD16—62no—
442C3×SD16—62no—
443C3×D8—32no—
444C3×D8—32no—
445C3×D8—61no—
446C3×D8—61no—
447C3×M16—22no—
448C3×M16—22no—
449C3×M16—42no—
450C3×M16—41no—
451C3×M16—41no—
452C3×M16—61no—
453C3×M16—61no—
454C3×M16—81no—
455C3×M16—124no—
456C2×C3×C8—21no—
457C2×C3×C8—21no—
458C2×C3×C8—21no—
459C2×C3×C8—21no—
460C2×C3×C8—21no—
461C2×C3×C8—21no—
462C2×C3×C8—32no—
463C2×C3×C8—41no—
464C2×C3×C8—41no—
465C2×C3×C8—81no—
466C2×C3×C8—124no—
467C2×C3×C8C2×C4×D311yescharacteristic
468C2×C3×C8C2×C4×D311yescharacteristic
469C2×C3×C8C2×C4×D311yescharacteristic
470C2×C3×C8C2×C4×D311yescharacteristic
471C2×C3×C8#23511yescharacteristic
472C2×C3×C8#23511yescharacteristic
473C2×C3×C8D3×D411yescharacteristic
474C2×C3×C8#23711yescharacteristic
475C2×C3×C8#23711yescharacteristic
476C2×C3×C8C2×#6711yescharacteristic
477C2×C3×C8C23×D311yescharacteristic
478C2×C3×C8C23×D311yescharacteristic
479C3×C4⋊C4—61no—
480C3×C22⋊C4—61no—
481C3×C42—32no—
482#217—21no—
483#217—122no—
484(C2×D3)⋊C4—122no—
485C4⋊Dic3—21no—
486C4⋊Dic3—62no—
487C4⋊Dic3—62no—
488C4⋊Dic3—122no—
489C4⋊Dic3—122no—
490C4⋊Dic3—121no—
491C4⋊Dic3—121no—
492C4⋊Dic3—241no—
493Dic3⋊C4—122no—
494C4×Dic3—122no—
495C4×Dic3—122no—
496C4×Dic3C2×#6712yes—
497#208—21no—
498#208—21no—
499C2×C3⋊C8C2×#6712yes—
500Dic12—21no—
501Dic12—21no—
502Dic12C2×C4×D312yes—
503Dic12C2×C4×D312yes—
504D24—21no—
505D24—21no—
506D24C2×C4×D312yes—
507D24C2×C4×D312yes—
508#204—22no—
509#204—22no—
510#204—22no—
511#204—22no—
512ΓL(1,𝔽25)—44no—
513D3×C8—44no—
514C3×C16—62no—
515C3⋊C16—22no—
516C3⋊C16—34no—
517C3⋊C16—34no—
518C3⋊C16—64no—
519C22×C32—41no—
520C22×C32#44211yescharacteristic
521C22×C32#44211yescharacteristic
522C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
523C2×C3×D3—42no—
524C2×C3×D3—42no—
525C2×C3×D3—81no—
526C2×C3×D3—81no—
527C2×C3×D3—161no—
528C32×C4#44211yescharacteristic
529C32×C4#44211yescharacteristic
530C32×C4C2×C4×D411yescharacteristic
531C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
532C3⋊Dic3—82no—
533C3×Dic3—42no—
534C3×Dic3—42no—
535C3×Dic3—42no—
536C2×#41—61no—
537C2×#41—61no—
538#135—32no—
539#135—32no—
540#135—32no—
541#135—32no—
542#135—61no—
543#135—61no—
544#135—61no—
545#135—61no—
546C2×Q16—31no—
547C2×Q16—31no—
548C2×SD16—61no—
549C2×SD16—61no—
550C2×D8—31no—
551C2×D8—31no—
552#131—64no—
553#131—122no—
554C2×M16—21no—
555C2×M16—31no—
556C2×M16—122no—
557C22×C8C2×D3211yescharacteristic
558C4×Q8—182no—
559C4×D4—182no—
560C4×D4—362no—
561#117—31no—
562#117—361no—
563C2×C4⋊C4—181no—
564C2×C4⋊C4—361no—
565Q32—94no—
566SD32—94no—
567SD32—94no—
568D16—94no—
569M32—32no—
570M32—61no—
571M32—92no—
572M32—92no—
573C2×C16—61no—
574C2×C16—92no—
575#108—21no—
576#108C2×D3212yes—
577#106—92no—
578#106—181no—
579#104—64no—
580#103—182no—
581#102—182no—
582#97—32no—
583C4×C8—32no—
584C23×C3—21no—
585C23×C3—121no—
586C23×C3—121no—
587C23×C3#91411yescharacteristic
588C23×C3#94911yescharacteristic
589C22×D3—41no—
590C22×D3—41no—
591C3×Q8—62no—
592C3×Q8—62no—
593C3×Q8—121no—
594C3×Q8—121no—
595C3×D4—62no—
596C3×D4—62no—
597C3×D4—122no—
598C3×D4—122no—
599C3×D4—122no—
600C3×D4—122no—
601C3×D4—121no—
602C3×D4—121no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—62no—
610C2×C3×C4—121no—
611C2×C3×C4—121no—
612C2×C3×C4—122no—
613C2×C3×C4—122no—
614C2×C3×C4—122no—
615C2×C3×C4—122no—
616C2×C3×C4#67⋊C411yescharacteristic
617C2×C3×C4#67⋊C411yescharacteristic
618C2×C3×C4#91111yescharacteristic
619C2×C3×C4#91111yescharacteristic
620C2×C3×C4#91411yescharacteristic
621C2×C3×C4C4×#6711yescharacteristic
622C2×C3×C4C4×#6711yescharacteristic
623C2×C3×C4#93211yescharacteristic
624C2×C3×C4#93211yescharacteristic
625C2×C3×C4#94911yescharacteristic
626C2×C3×C4C2×D3×D411yescharacteristic
627C2×C3×C4C22×#6711yescharacteristic
628#67—42no—
629#67—42no—
630#67—42no—
631#67—42no—
632C2×Dic3—22no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—122no—
636C2×Dic3—122no—
637C2×Dic3—242no—
638C2×Dic3—482no—
639C2×Dic3—481no—
640C2×Dic3—481no—
641C2×Dic3—482no—
642D12—22no—
643D12—22no—
644D12—41no—
645D12—41no—
646C4×D3—42no—
647C4×D3—42no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—482no—
651Dic6—22no—
652Dic6—22no—
653Dic6—41no—
654Dic6—41no—
655C3×C8—21no—
656C3×C8—21no—
657C3×C8—21no—
658C3×C8—21no—
659C3×C8—42no—
660C3×C8—42no—
661C3×C8—62no—
662C3×C8—82no—
663C3×C8#67⋊C411yescharacteristic
664C3×C8#67⋊C411yescharacteristic
665C3×C8C4×#6711yescharacteristic
666C3×C8C4×#6711yescharacteristic
667C3×C8C22×C4×D311yescharacteristic
668C3×C8C22×C4×D311yescharacteristic
669C3×C8C2×#23511yescharacteristic
670C3×C8C2×#23711yescharacteristic
671C3⋊C8—22no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32C2×#44211yescharacteristic
676C3×D3—82no—
677C3×D3—82no—
678#41—62no—
679#41—62no—
680#41—62no—
681#41—62no—
682#41—121no—
683#41—121no—
684#41—121no—
685#41—121no—
686C2×Q8—61no—
687C2×Q8—61no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—121no—
691C2×D4—121no—
692C22×C4—121no—
693C22×C4—121no—
694C22×C4—362no—
695C22×C4—361no—
696C22×C4D3×#6711yescharacteristic
697Q16—32no—
698Q16—32no—
699Q16—61no—
700Q16—61no—
701SD16—62no—
702SD16—62no—
703SD16—62no—
704SD16—62no—
705D8—32no—
706D8—32no—
707D8—61no—
708D8—61no—
709M16—22no—
710M16—41no—
711M16—61no—
712M16—61no—
713M16—124no—
714C2×C8—32no—
715C2×C8—41no—
716C2×C8—124no—
717C2×C8#379511yescharacteristic
718C2×C8#379511yescharacteristic
719C2×C8C4×D3211yescharacteristic
720C2×C8C4×D3211yescharacteristic
721C2×C8D3×#6711yescharacteristic
722C2×C8C22×D3211yescharacteristic
723C4⋊C4—61no—
724C4⋊C4—182no—
725C4⋊C4—362no—
726C4⋊C4—361no—
727C22⋊C4—61no—
728C22⋊C4—362no—
729C42—32no—
730C42—362no—
731C16—62no—
732C16—94no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—42no—
739C22×C3—122no—
740C22×C3—122no—
741C22×C3—241no—
742C22×C3—241no—
743C22×C3—481no—
744C22×C3#478511yescharacteristic
745C22×C3#478511yescharacteristic
746C22×C3#501411yescharacteristic
747C22×C3#501411yescharacteristic
748C22×C3C2×#91411yescharacteristic
749C22×C3C2×#94911yescharacteristic
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—81no—
753C2×D3—81no—
754C2×D3—161no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—122no—
760C3×C4—122no—
761C3×C4—122no—
762C3×C4#478511yescharacteristic
763C3×C4#478511yescharacteristic
764C3×C4#501411yescharacteristic
765C3×C4#501411yescharacteristic
766C3×C4C2×#67⋊C411yescharacteristic
767C3×C4C2×#91111yescharacteristic
768C3×C4C2×C4×#6711yescharacteristic
769C3×C4C2×#93211yescharacteristic
770Dic3—42no—
771Dic3—42no—
772Dic3—42no—
773Dic3—242no—
774Dic3—242no—
775Dic3—482no—
776C32#3346911yescharacteristic, complemented, Sylow
777C23—121no—
778C23—121no—
779C23#6393911yescharacteristic
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—62no—
785D4—62no—
786D4—122no—
787D4—122no—
788D4—122no—
789D4—122no—
790D4—121no—
791D4—121no—
792C2×C4—62no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—122no—
796C2×C4—122no—
797C2×C4—122no—
798C2×C4—122no—
799C2×C4—362no—
800C2×C4—1442no—
801C2×C4—1441no—
802C2×C4#6387911yescharacteristic
803C2×C4#6387911yescharacteristic
804C2×C4#6393211yescharacteristic
805C2×C4#6393211yescharacteristic
806C2×C4#6393911yescharacteristic
807C2×C4C2×D3×#6711yescharacteristic
808C8—42no—
809C8—62no—
810C8#6387911yescharacteristic
811C8#6387911yescharacteristic
812C8C2×#379511yescharacteristic
813C8C2×C4×D3211yescharacteristic
814C2×C3—22no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—242no—
825C2×C3—242no—
826C2×C3C2×#478511yescharacteristic
827C2×C3C2×#501411yescharacteristic
828D3—82no—
829D3—82no—
830C22—41no—
831C22—122no—
832C22—122no—
833C22—241no—
834C22—241no—
835C22—481no—
836C22#1059045511yescharacteristic
837C22#1059045511yescharacteristic
838C22C2×#6393911yescharacteristic
839C4—122no—
840C4—122no—
841C4—122no—
842C4—722no—
843C4#1059045511yescharacteristic
844C4#1059045511yescharacteristic
845C4C2×#6387911yescharacteristic
846C4C2×#6393211yescharacteristic
847C3—21no—
848C3#1094864611yescharacteristic, complemented
849C3#1094864911yescharacteristic, complemented
850C2—21no—
851C2—21no—
852C2—21no—
853C2—242no—
854C2—242no—
855C2C2×#1059045511yescharacteristic
subgroupG/H
centerC2C2×#10590455
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC2×C32×#108C22
socleC2×C32C2×#442
prime radical#11899653C2
cosocleC2×C32×C8C24
hypercenterC2×#108D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C3×#79249C2semidirect
3. #11860967C2semidirect
4. #11797981C2semidirect
5. #11797935C2semidirect
6. C2×#10589360C2semidirect
7. C3×#70687C2semidirect
8. C2×#10589124C2semidirect
9. #11795946C2semidirect
25. #10590812C22semidirect
26. #10590771C22semidirect
28. #10590636C4semidirect
30. #10590630C4semidirect
32. #10590629C4semidirect
33. #10589360C22semidirect
34. C3×#4496C22semidirect
35. C3×#4495C22semidirect
37. #10589105C22semidirect
42. #79249D3semidirect
50. #70687D3semidirect
66. C2×C3×Dic12C2×C4semidirect
74. C3×#904C2×C4semidirect
76. C2×C3×D24C2×C4semidirect
90. #63639C2×C4semidirect
92. C2×C3⋊(C3⋊C16)C2×C4semidirect
101. #63550C2×C4semidirect
102. #63547C2×C4semidirect
103. #63547C2×C4semidirect
104. #63545C2×C4semidirect
156. #4496C2×D3semidirect
157. #4495C2×D3semidirect
267. C2×Dic12C4×D3semidirect
275. #904C4×D3semidirect
277. C2×D24C4×D3semidirect
776. C32#33469semidirect
848. C3#10948646semidirect
849. C3#10948649semidirect

Maximal subgroups

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

subgroupindex
#118996532
C3×#792492
#118609672
#117979812
#117979352
C2×#105893602
C3×#706872
C2×#105891242
#117959462
#109486493
#109486463