Finite Group Databasebeta

← #11860749

Subgroups — #11860749

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596016C211yesmaximal, characteristic
2C2×#63930C211yesmaximal, characteristic
3#10593848C211yesmaximal, characteristic, complemented
4C3×#5018C211yesmaximal, characteristic, complemented
5C3×C4×#214C211yesmaximal, characteristic, complemented
6#10591446C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591426C211yesmaximal, characteristic
9#10590602C211yesmaximal, characteristic, complemented
10#10590574C211yesmaximal, characteristic, complemented
11#10590484C211yesmaximal, characteristic, complemented
12#10590483C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#79649—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×#3752—21no—
24#64102C2211yescharacteristic
25#64101C2211yescharacteristic
26#64090—21no—
27C22⋊C4×C3⋊D3—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64081C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63930C418yescomplemented
35#63849C2211yescharacteristic
36#63843C2211yescharacteristic, complemented
37#63843C2211yescharacteristic, complemented
38#63837—21no—
39#63837—21no—
40#63836—21no—
41#63836—21no—
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#803C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#63553C2211yescharacteristic, complemented
62C2×D3×SD16—31no—
63C2×D3×SD16—31no—
64#5572—31no—
65#5572—31no—
66#5545—31no—
67#5545—31no—
68#5545—61no—
69C3×#440—31no—
70C3×C4×SD16—31no—
71#5164—31no—
72Dic3×SD16—31no—
73#5026—31no—
74C4×#215—31no—
75#5018D311yescharacteristic, complemented
76C4×#214D311yescharacteristic, complemented
77#4889—31no—
78#4880—31no—
79#4860—31no—
80#4852—31no—
81#4817—31no—
82#4802—31no—
83#4802—31no—
84#4788—31no—
85#4770—31no—
86#4770—31no—
87#4758—31no—
88#4757—31no—
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C23×C3⋊D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98D4×C3⋊D3—22no—
99D4×C3⋊D3C2×C414yes—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#624—21no—
108#3797—22no—
109#3797C2×C414yescomplemented
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113#3757—21no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752D411yescharacteristic
118#3752D411yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750D411yescharacteristic
121#3750D411yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#214C2×C414yescomplemented
125C3×#214C2×C414yescomplemented
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3717C2×C414yescomplemented
144#3712—22no—
145#3710C2×C414yescomplemented
146#2949—91noSylow
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×D4—31no—
150C2×D3×D4—31no—
151C2×D3×D4—61no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—21no—
157C3×C4×D4C2×D311yescharacteristic
158C3×C4×D4C2×D311yescharacteristic
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166C2×#214C2×D311yescharacteristic
167C2×#214C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—62no—
171C2×(C2×D3)⋊C4—61no—
172C2×(C2×D3)⋊C4—61no—
173C2×(C2×D3)⋊C4—62no—
174D3×SD16—38no—
175D3×SD16—38no—
176C2×#204—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×ΓL(1,𝔽25)—31no—
180C2×D3×C8—31no—
181C2×D3×C8—31no—
182#893—31no—
183#893—31no—
184#893—61no—
185#892—31no—
186#892—31no—
187#892—31no—
188#892—31no—
189#892—61no—
190#892—61no—
191#892—61no—
192#887—31no—
193#887—31no—
194#887—61no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—62no—
199D3×C22⋊C4—61no—
200D3×C22⋊C4—61no—
201D3×C22⋊C4—62no—
202C4×D12—31no—
203C4×D12—31no—
204C4×D12—61no—
205#872—31no—
206#872—31no—
207#872—61no—
208#872—61no—
209#872—61no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6C2×D311yescharacteristic, complemented
213C4×Dic6C2×D311yescharacteristic, complemented
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#835—31no—
224#832C2×D311yescharacteristic
225#832C2×D311yescharacteristic
226#821—31no—
227#821—31no—
228#818—31no—
229#817—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic, complemented
237#810C2×D311yescharacteristic, complemented
238#809—31no—
239#809—31no—
240#808—31no—
241#808C2×D311yescharacteristic, complemented
242#807—31no—
243#807C2×D311yescharacteristic, complemented
244#803C2×D311yescharacteristic, complemented
245C4×C3⋊C8C2×D311yescharacteristic, complemented
246C23×C32—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—24no—
249C22×C3⋊D3—81no—
250C22×C3⋊D3—81no—
251C22×C3⋊D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4C22×C412yes—
254C2×C32×C4—21no—
255C2×C32×C4—81no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259#638—24no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—81no—
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)C22×C412yes—
267C4×C3⋊D3—81no—
268C4×C3⋊D3—81no—
269C4×C3⋊D3C22×C412yes—
270C4×C3⋊D3#4112yes—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6C22×C412yes—
278C3×Dic6C22×C412yes—
279#627—24no—
280#624—24no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C3×C3⋊C8C22×C412yes—
285C22×SD16—91no—
286#519—91no—
287#518—91no—
288#440—31no—
289#440—91no—
290#440—91no—
291#440—91no—
292C4×SD16—31no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296#427—91no—
297#419—91no—
298#418—91no—
299#405—91no—
300C23×D3—61no—
301C23×D3—61no—
302C23×D3—62no—
303C2×C3×Q8—31no—
304C2×C3×Q8—31no—
305C2×C3×D4—21no—
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C22×C3×C4—22no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—62no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—62no—
317D3×Q8—34no—
318D3×Q8—34no—
319D3×Q8—62no—
320D3×Q8—62no—
321D3×D4—34no—
322D3×D4—34no—
323D3×D4—64no—
324D3×D4—62no—
325D3×D4—62no—
326D3×D4—64no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×C4×D3—31no—
331C2×C4×D3—31no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—62no—
338C2×C4×D3—62no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C2×Dic6C22×D311yescharacteristic
345C3×SD16—34no—
346C3×SD16—34no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C22⋊C4—22no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C42—21no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42C22×D311yescharacteristic
365C3×C42C22×D311yescharacteristic
366#217—61no—
367#217—61no—
368#217—62no—
369#215—34no—
370#215—34no—
371#214C4×D314yescomplemented
372#214C4×D314yescomplemented
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407C4×Dic3—21no—
408C4×Dic3—21no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—62no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425#204—34no—
426#204—34no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429D3×C8—34no—
430D3×C8—34no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—22no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—84no—
441C2×C3⋊D3C4×D412yes—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—41no—
445C32×C4C23×C411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3C4×D412yes—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C22×Q8—91no—
456C22×D4—91no—
457C2×SD16—31no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×SD16—91no—
461C2×SD16—98no—
462C2×M16—91no—
463C22×C8—91no—
464C4×Q8—31no—
465C4×Q8—31no—
466C4×Q8—91no—
467C4×Q8—91no—
468C4×Q8—181no—
469C4×Q8—181no—
470C4×D4—91no—
471C4×D4—91no—
472C4×D4—91no—
473C4×D4—181no—
474C4×D4—181no—
475C4×D4D3211yescharacteristic
476#117—91no—
477#117—91no—
478#117—91no—
479#117—181no—
480#117—181no—
481C2×C22⋊C4—181no—
482C2×C22⋊C4—181no—
483#107—31no—
484#107—91no—
485#106—31no—
486#106—91no—
487#103—31no—
488#103—31no—
489#103—91no—
490#103—91no—
491#102—31no—
492#102—31no—
493#102—91no—
494#102—91no—
495#97—31no—
496#97—91no—
497C4×C8—31no—
498C4×C8—91no—
499C23×C3—22no—
500C23×C3—21no—
501C23×C3—21no—
502C22×D3—31no—
503C22×D3—31no—
504C22×D3—61no—
505C22×D3—64no—
506C22×D3—64no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—68no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3—241no—
515C22×D3—242no—
516C22×D3—242no—
517C3×Q8—32no—
518C3×Q8—32no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—22no—
525C3×D4C2×C4×D312yes—
526C3×D4C2×C4×D312yes—
527C2×C3×C4—22no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—81no—
538C2×C3×C4—81no—
539C2×C3×C4—82no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4D3×D411yescharacteristic
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4D3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—64no—
547#67—64no—
548#67—68no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—242no—
568D12—32no—
569D12—32no—
570D12—62no—
571D12—62no—
572D12—61no—
573D12—61no—
574C4×D3—32no—
575C4×D3—32no—
576C4×D3—32no—
577C4×D3—32no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—64no—
581C4×D3—64no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C4×D3—241no—
586C4×D3—242no—
587C4×D3—242no—
588Dic6—21no—
589Dic6—21no—
590Dic6—64no—
591Dic6—64no—
592Dic6C2×C4×D312yes—
593Dic6C2×C4×D312yes—
594C3×C8—32no—
595C3×C8—32no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8C2×C4×D312yes—
601C3⋊C8C2×C4×D312yes—
602C2×C32—42no—
603C2×C32C2×C4×D411yescharacteristic
604C2×C32#57711yescharacteristic
605C2×C32#57711yescharacteristic
606C3⋊D3—22no—
607C3⋊D3—42no—
608C24—181no—
609C2×Q8—31no—
610C2×Q8—31no—
611C2×Q8—94no—
612C2×Q8—181no—
613C2×Q8—182no—
614C2×D4—94no—
615C2×D4—91no—
616C2×D4—182no—
617C2×D4—181no—
618C2×D4C2×D3211yescharacteristic
619C22×C4—21no—
620C22×C4—91no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625SD16—34no—
626SD16—34no—
627SD16—94no—
628SD16—94no—
629M16—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—31no—
634C2×C8—94no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—61no—
654C42—61no—
655C42—91no—
656C42—181no—
657C42—181no—
658C42—181no—
659C42—181no—
660C42C2×D3211yescharacteristic
661C22×C3—24no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—62no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—64no—
681C2×D3—62no—
682C2×D3—62no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—122no—
686C2×D3—122no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—244no—
692C2×D3—244no—
693C2×D3—248no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—42no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—62no—
706C3×C4—62no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C22×C4×D311yescharacteristic
710C3×C4C22×C4×D311yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—22no—
714Dic3—22no—
715Dic3—32no—
716Dic3—32no—
717Dic3—41no—
718Dic3—41no—
719Dic3—62no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—121no—
725Dic3—121no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729C32#294911yescharacteristic, complemented, Sylow
730C23—21no—
731C23—91no—
732C23—184no—
733C23—181no—
734C23—721no—
735C23—721no—
736Q8—32no—
737Q8—32no—
738Q8—61no—
739Q8—61no—
740Q8—184no—
741D4—21no—
742D4—92no—
743D4—184no—
744D4—181no—
745D4C4×D3212yes—
746C2×C4—21no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—81no—
752C2×C4—91no—
753C2×C4—92no—
754C2×C4—92no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—184no—
758C2×C4—181no—
759C2×C4—721no—
760C2×C4—721no—
761C2×C4—721no—
762C2×C4#381111yescharacteristic
763C2×C4#381111yescharacteristic
764C2×C4C22×D3211yescharacteristic
765C8—32no—
766C8—32no—
767C8—61no—
768C8—61no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—44no—
773C2×C3—42no—
774C2×C3—42no—
775C2×C3C4×D3×D411yescharacteristic
776C2×C3C4×D3×D411yescharacteristic
777C2×C3#576211yescharacteristic
778C2×C3#577011yescharacteristic
779C2×C3#577511yescharacteristic
780C2×C3#577811yescharacteristic
781D3—62no—
782D3—62no—
783D3—122no—
784D3—124no—
785D3—122no—
786D3—122no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—92no—
791C22—181no—
792C22—181no—
793C22—182no—
794C22—361no—
795C22—361no—
796C22—724no—
797C22C2×#381111yescharacteristic
798C4—21no—
799C4—21no—
800C4—41no—
801C4—62no—
802C4—62no—
803C4—92no—
804C4—121no—
805C4—121no—
806C4—181no—
807C4—181no—
808C4—361no—
809C4C2×C4×D3211yescharacteristic
810C4#6430611yescharacteristic
811C3—21no—
812C3#7964911yescharacteristic, complemented
813C3#7977711yescharacteristic, complemented
814C2—42no—
815C2—182no—
816C2—362no—
817C2C4×#381111yescharacteristic
818C2#1059511511yescharacteristic
819C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593848C2semidirect
4. C3×#5018C2semidirect
5. C3×C4×#214C2semidirect
6. #10591446C2semidirect
7. #10591445C2semidirect
9. #10590602C2semidirect
10. #10590574C2semidirect
11. #10590484C2semidirect
12. #10590483C2semidirect
13. #10590362C2semidirect
14. C4×#3717C2semidirect
15. #10590321C2semidirect
32. C3×C4×Dic6C22semidirect
33. C3×C4×Dic6C22semidirect
34. #63930C4semidirect
36. #63843C22semidirect
37. #63843C22semidirect
48. C3×#810C22semidirect
49. C3×#810C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#803C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63566C22semidirect
57. #63566C22semidirect
60. #63555C22semidirect
61. #63553C22semidirect
75. #5018D3semidirect
76. C4×#214D3semidirect
109. #3797C2×C4semidirect
124. C3×#214C2×C4semidirect
125. C3×#214C2×C4semidirect
142. #3717C2×C4semidirect
143. #3717C2×C4semidirect
145. #3710C2×C4semidirect
212. C4×Dic6C2×D3semidirect
213. C4×Dic6C2×D3semidirect
236. #810C2×D3semidirect
237. #810C2×D3semidirect
241. #808C2×D3semidirect
243. #807C2×D3semidirect
244. #803C2×D3semidirect
245. C4×C3⋊C8C2×D3semidirect
371. #214C4×D3semidirect
372. #214C4×D3semidirect
729. C32#2949semidirect
812. C3#79649semidirect
813. C3#79777semidirect

Maximal subgroups

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

subgroupindex
#105960162
C2×#639302
#105938482
C3×#50182
C3×C4×#2142
#105914462
#105914452
#105914262
#105906022
#105905742
#105904842
#105904832
#105903622
C4×#37172
#105903212
#797773
#796493