Finite Group Databasebeta

← #11872203

Subgroups — #11872203

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2#10594984C211yesmaximal, characteristic, complemented
3C3×#5003C211yesmaximal, characteristic, complemented
4C3×#4996C211yesmaximal, characteristic, complemented
5#10591183C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic
7#10591062C211yesmaximal, characteristic, complemented
8#10590540C211yesmaximal, characteristic, complemented
9#10590540C211yesmaximal, characteristic, complemented
10#10590484C211yesmaximal, characteristic, complemented
11#10590483C211yesmaximal, characteristic, complemented
12#10590462C211yesmaximal, characteristic, complemented
13#10590459C211yesmaximal, characteristic, complemented
14#10590433C211yesmaximal, characteristic, complemented
15#10590430C211yesmaximal, characteristic, complemented
16#81496—31nomaximal
17#81352—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64135C2211yescharacteristic
21#64102C2211yescharacteristic
22#64102C2211yescharacteristic
23#64102C2211yescharacteristic
24#64102C2211yescharacteristic
25C22⋊C4×C3⋊D3—21no—
26C22⋊C4×C3⋊D3—21no—
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)—21no—
29C3×#930C2211yescharacteristic
30C3×#924C2211yescharacteristic
31#63969—21no—
32#63959—21no—
33#63919C2211yescharacteristic, complemented
34#63898C2211yescharacteristic, complemented
35#63893—21no—
36#63863C2211yescharacteristic, complemented
37#63861—21no—
38#63843C2211yescharacteristic, complemented
39C2×#3717C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×#830C2211yescharacteristic
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5643—31no—
62#5603—31no—
63#5521—31no—
64#5521—31no—
65#5521—61no—
66C3×#485—31no—
67C3×#482—31no—
68#5046—31no—
69#5036—31no—
70#5003D311yescharacteristic, complemented
71#4996D311yescharacteristic, complemented
72#4890—31no—
73#4890—31no—
74#4889—31no—
75#4872—31no—
76#4870—31no—
77#4870—31no—
78#4869—31no—
79#4852—31no—
80#4819—31no—
81#4819—31no—
82#4817—31no—
83#4788—31no—
84#4787—31no—
85#4787—31no—
86#4785—31no—
87#4756—31no—
88#4732—31no—
89#4731—31no—
90#4720—31no—
91#4720—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C42—21no—
112#3757D411yescharacteristic
113#3757D411yescharacteristic
114#3752—21no—
115#3752—21no—
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)D411yescharacteristic
119C4⋊(C3⋊Dic3)D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3717—22no—
138#3717—22no—
139#3714—22no—
140#3714—22no—
141#3118—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×C22⋊Q8—31no—
146C3×#121—31no—
147C3×#117—21no—
148C3×#117C2×D311yescharacteristic
149C3×#117C2×D311yescharacteristic
150#947—31no—
151Q8×Dic3—31no—
152C2×#215—31no—
153C2×#215—31no—
154#936—31no—
155#936—61no—
156#935—61no—
157D4×Dic3—31no—
158C2×#213—31no—
159C2×#213—31no—
160#930C2×D311yescharacteristic
161#926—31no—
162#926—31no—
163#926—61no—
164#924C2×D311yescharacteristic
165C2×D24—31no—
166C2×D24—31no—
167C2×#204—31no—
168C2×#204—31no—
169#898—61no—
170#897—61no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—61no—
181#893—61no—
182#893—61no—
183#893—61no—
184#888—31no—
185#888—31no—
186#887—31no—
187#885—61no—
188#883—61no—
189D3×C22⋊C4—61no—
190D3×C22⋊C4—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193D3×C22⋊C4—62no—
194D3×C22⋊C4—62no—
195#879—61no—
196#878—61no—
197C4×D12—61no—
198C4×D12—61no—
199C4×D12—61no—
200C4×D12—61no—
201C4×D12—62no—
202C4×D12—62no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#106—31no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C22⋊C8—31no—
212C3×C22⋊C8—31no—
213#830C2×D311yescharacteristic
214#830C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#815—31no—
220#815—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227#810C2×D311yescharacteristic, complemented
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809C2×D311yescharacteristic, complemented
234#809C2×D311yescharacteristic, complemented
235#808C2×D311yescharacteristic, complemented
236#808C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238#807C2×D311yescharacteristic, complemented
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—24no—
243C22×C3⋊D3—81no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C4⋊(C3⋊D3)—24no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)#4112yes—
260C4⋊(C3⋊D3)#4112yes—
261C4×C3⋊D3—81no—
262C4×C3⋊D3—81no—
263C4×C3⋊D3—81no—
264C4×C3⋊D3—81no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#627—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#542—91no—
280#518—91no—
281#485—31no—
282#482—31no—
283#476—91no—
284#474—91no—
285#463—91no—
286#463—91no—
287#450—91no—
288#447—91no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C23×D3—62no—
295C23×D3—61no—
296C23×D3—61no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—21no—
304C22×Dic3—61no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×D12—61no—
311C2×D12—62no—
312C2×D12—62no—
313C2×D12—62no—
314C2×D12—62no—
315C2×D12—62no—
316C2×D12—64no—
317C2×D12—64no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—62no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—22no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—22no—
356C3×C42—21no—
357C3×C42—21no—
358#217—21no—
359#217—31no—
360#217—31no—
361#217—31no—
362#217—31no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#215—62no—
369#215—62no—
370#213—62no—
371#213—62no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
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—62no—
385(C2×D3)⋊C4—62no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
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—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412C2×C3⋊C8C22×D311yescharacteristic
413D24—62no—
414D24—62no—
415#204—62no—
416#204—62no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—84no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—21no—
439C3⋊Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—91no—
449#126—181no—
450#124—91no—
451#124—181no—
452#123—181no—
453C22⋊Q8—31no—
454C22⋊Q8—181no—
455#121—31no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4—181no—
464#117—91no—
465#117D3211yescharacteristic
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—31no—
469#107—31no—
470#106—31no—
471#106—31no—
472C4⋊C8—91no—
473C4⋊C8—91no—
474#103—31no—
475#103—31no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—91no—
485C4×C8—91no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3D3×D411yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—62no—
492C22×D3—62no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—68no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—241no—
501C22×D3—241no—
502C22×D3—241no—
503C22×D3—241no—
504C22×D3—242no—
505C22×D3—242no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—241no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—81no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—241no—
549D12—21no—
550D12—21no—
551D12—32no—
552D12—32no—
553D12—32no—
554D12—32no—
555D12—62no—
556D12—62no—
557D12—68no—
558D12—64no—
559D12—64no—
560D12—62no—
561D12—62no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C4×D3—242no—
576C4×D3—242no—
577C4×D3—242no—
578C4×D3—242no—
579Dic6—21no—
580Dic6—21no—
581Dic6—241no—
582Dic6—241no—
583C3×C8—61no—
584C3×C8—61no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32#52511yescharacteristic
593C2×C32#57611yescharacteristic
594C2×C32#57711yescharacteristic
595C3⋊D3—42no—
596C3⋊D3—42no—
597C3×D3—81no—
598C24—181no—
599C2×Q8—31no—
600C2×Q8—181no—
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—182no—
606C2×D4—182no—
607C2×D4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—182no—
615SD16—182no—
616D8—182no—
617D8—182no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—21no—
644C42—91no—
645C42—91no—
646C42—181no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3C2×D3×D411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—64no—
666C2×D3—64no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—248no—
684C2×D3—244no—
685C2×D3—244no—
686C3×C4—22no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—61no—
708Dic3—61no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719C32#311811yescharacteristic, complemented, Sylow
720C23—61no—
721C23—184no—
722C23—181no—
723C23—181no—
724C23—721no—
725C23—721no—
726C23#381111yescharacteristic
727Q8—61no—
728Q8—61no—
729Q8—721no—
730D4—61no—
731D4—61no—
732D4—92no—
733D4—92no—
734D4—184no—
735D4—181no—
736D4—181no—
737D4—241no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—91no—
748C2×C4—91no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4#381111yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—241no—
767C2×C3#565611yescharacteristic
768C2×C3#565611yescharacteristic
769C2×C3#576911yescharacteristic
770C2×C3#577011yescharacteristic
771C2×C3#577411yescharacteristic
772C2×C3#577811yescharacteristic
773D3—81no—
774D3—124no—
775D3—124no—
776D3—122no—
777D3—122no—
778D3—122no—
779D3—122no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—182no—
787C22—182no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—361no—
792C22—724no—
793C22C2×#381111yescharacteristic
794C4—21no—
795C4—41no—
796C4—41no—
797C4—121no—
798C4—121no—
799C4—121no—
800C4—181no—
801C4—181no—
802C4—181no—
803C4—181no—
804C4#6430611yescharacteristic
805C4#6430611yescharacteristic
806C3—21no—
807C3#8135211yescharacteristic, complemented
808C3#8149611yescharacteristic, complemented
809C2—41no—
810C2—241no—
811C2—362no—
812C2—362no—
813C2#1059492011yescharacteristic
814C2#1059546111yescharacteristic
815C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10591168C2
hypercenter#117D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
2. #10594984C2semidirect
3. C3×#5003C2semidirect
4. C3×#4996C2semidirect
5. #10591183C2semidirect
7. #10591062C2semidirect
8. #10590540C2semidirect
9. #10590540C2semidirect
10. #10590484C2semidirect
11. #10590483C2semidirect
12. #10590462C2semidirect
13. #10590459C2semidirect
14. #10590433C2semidirect
15. #10590430C2semidirect
33. #63919C22semidirect
34. #63898C22semidirect
36. #63863C22semidirect
38. #63843C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
70. #5003D3semidirect
71. #4996D3semidirect
227. #810C2×D3semidirect
228. #810C2×D3semidirect
233. #809C2×D3semidirect
234. #809C2×D3semidirect
235. #808C2×D3semidirect
236. #808C2×D3semidirect
237. #807C2×D3semidirect
238. #807C2×D3semidirect
719. C32#3118semidirect
807. C3#81352semidirect
808. C3#81496semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105949842
C3×#50032
C3×#49962
#105911832
#105911682
#105910622
#105905402
#105904842
#105904832
#105904622
#105904592
#105904332
#105904302
#814963
#813523