Finite Group Databasebeta

← #11872294

Subgroups — #11872294

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2#10595041C211yesmaximal, characteristic, complemented
3C3×#5238C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5#10591622C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10591486C211yesmaximal, characteristic, complemented
10#10591479C211yesmaximal, characteristic, complemented
11#10591436C211yesmaximal, characteristic, complemented
12#10591435C211yesmaximal, characteristic, complemented
13#10591094C211yesmaximal, characteristic, complemented
14#10591092C211yesmaximal, characteristic, complemented
15#10591062C211yesmaximal, characteristic, complemented
16#80073—31nomaximal
17#80072—31nomaximal
18C2×C32×#41C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25#64135—21no—
26#64135C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)—21no—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#930C2211yescharacteristic
35#63970—21no—
36#63970—21no—
37#63914C2211yescharacteristic
38#63898C2211yescharacteristic
39#63898C2211yescharacteristic
40#63891—21no—
41#63891—21no—
42#63872C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5827—31no—
62#5827—31no—
63#5827—61no—
64#5619—31no—
65#5619—31no—
66C3×#449—31no—
67C3×#449—31no—
68#5238D311yescharacteristic, complemented
69#5238D311yescharacteristic, complemented
70#5164—31no—
71#5163—31no—
72#5163—31no—
73Dic3×SD16—31no—
74#5152—31no—
75#5150—31no—
76#5150—31no—
77Dic3×D8—31no—
78#5034—31no—
79#5033—31no—
80#4817—31no—
81#4799—31no—
82#4796—31no—
83#4788—31no—
84#4785—31no—
85#4766—31no—
86#4763—31no—
87#4756—31no—
88#4736—31no—
89#4735—31no—
90#4720—31no—
91#4720—31no—
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C22×C3⋊Dic3—21no—
101C22×C3⋊Dic3—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3757—21no—
111#3757—21no—
112#3757D411yescharacteristic
113#3757D411yescharacteristic
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)D411yescharacteristic
118C4⋊(C3⋊Dic3)D411yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#215—22no—
126C3×#215—22no—
127C3×#213—22no—
128C3×#213—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3119—91noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C2×C3×D8—31no—
149C3×#121—31no—
150C3×#121—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—61no—
156Q8×Dic3—61no—
157C2×#215C2×D311yescharacteristic
158C2×#215C2×D311yescharacteristic
159#940—31no—
160#940—31no—
161#939—61no—
162#939—61no—
163#938—61no—
164#938—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174D4×Dic3—61no—
175D4×Dic3—61no—
176D4×Dic3—61no—
177D4×Dic3—62no—
178D4×Dic3—62no—
179C2×#213C2×D311yescharacteristic
180C2×#213C2×D311yescharacteristic
181#930C2×D311yescharacteristic
182#930C2×D311yescharacteristic
183#926—31no—
184#926—31no—
185#926—61no—
186#926—61no—
187#926—61no—
188#926—62no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192C2×C4⋊Dic3—61no—
193C2×C4⋊Dic3—61no—
194C2×C4⋊Dic3—62no—
195#893—31no—
196#893—31no—
197#890—31no—
198#890—31no—
199#886—61no—
200#886—61no—
201#883—61no—
202#883—61no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209#835C2×D311yescharacteristic
210#835C2×D311yescharacteristic
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830C2×D311yescharacteristic
218#830C2×D311yescharacteristic
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#818—31no—
224#818—31no—
225#817—31no—
226#817—31no—
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C32×Q8—21no—
244C32×Q8#4112yes—
245C32×D4—24no—
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—24no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C2×C3⋊Dic3—81no—
258C2×C3⋊Dic3—81no—
259C2×C3⋊Dic3C2×D411yescharacteristic
260C2×C3⋊Dic3C2×D411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C3×#67—81no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271#625—81no—
272#625—81no—
273D3×Dic3—81no—
274D3×Dic3—81no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#540—91no—
280#520—91no—
281#481—91no—
282#480—91no—
283#479—91no—
284#478—91no—
285#460—91no—
286#459—91no—
287#449—31no—
288#449—31no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C3×#41—24no—
295C3×#41—24no—
296C3×#41—22no—
297C3×#41—22no—
298C3×#41—22no—
299C3×#41—22no—
300C2×C3×Q8—21no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C22×C3×C4—22no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—62no—
334C22×Dic3—61no—
335C22×Dic3—61no—
336C2×D12C22×D311yescharacteristic
337C2×D12C22×D311yescharacteristic
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C3×SD16—62no—
341C3×SD16—62no—
342C3×D8—62no—
343C3×D8—62no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352#217—31no—
353#217—31no—
354#217—31no—
355#217—31no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—62no—
365#217—62no—
366#215—22no—
367#215—22no—
368#213—22no—
369#213—22no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—62no—
393C4⋊Dic3—62no—
394C4⋊Dic3—62no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
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—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—62no—
412C4×Dic3—62no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32C22×D411yescharacteristic
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C32×C4—21no—
431C32×C4—22no—
432C32×C4C2×#4111yescharacteristic
433C32×C4C2×#4111yescharacteristic
434C3⋊Dic3—21no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—41no—
439C3⋊Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41D3211yescharacteristic
443C2×SD16—31no—
444C2×SD16—31no—
445C2×D8—31no—
446C2×D8—31no—
447#127—91no—
448#125—91no—
449#123—181no—
450#123—181no—
451#121—31no—
452#121—31no—
453#121—181no—
454#121—181no—
455C4×Q8—91no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463#117—91no—
464#117—181no—
465C2×C4⋊C4—91no—
466C2×C4⋊C4—181no—
467#107—91no—
468#107—91no—
469#106—91no—
470#106—91no—
471C4⋊C8—91no—
472C4⋊C8—91no—
473#103—31no—
474#103—31no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481C22⋊C8—31no—
482C22⋊C8—31no—
483#97—91no—
484C4×C8—91no—
485C23×C3—22no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3D3×D411yescharacteristic
492C23×C3D3×D411yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C3×Q8—22no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—22no—
499C3×Q8#23712yes—
500C3×Q8#23712yes—
501C3×D4—28no—
502C3×D4—24no—
503C3×D4—24no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—241no—
513C3×D4—241no—
514C3×D4#23712yes—
515C3×D4#23712yes—
516C2×C3×C4—22no—
517C2×C3×C4—28no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—81no—
537#67—81no—
538#67—241no—
539#67—241no—
540#67—241no—
541#67—241no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—241no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—241no—
568C2×Dic3—241no—
569C2×Dic3—241no—
570C2×Dic3—242no—
571C2×Dic3—242no—
572C2×Dic3—242no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577C4×D3—241no—
578C4×D3—241no—
579C3×C8—61no—
580C3×C8—61no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32—41no—
588C2×C32—42no—
589C2×C32#52511yescharacteristic
590C2×C32#57611yescharacteristic
591C2×C32#57711yescharacteristic
592C3×D3—81no—
593C3×D3—81no—
594#41—22no—
595#41—22no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—21no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—21no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—62no—
613SD16—62no—
614D8—62no—
615D8—62no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—91no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—91no—
640C42—91no—
641C42—181no—
642C42—181no—
643C22×C3—22no—
644C22×C3—24no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3C2×D3×D411yescharacteristic
669C22×C3C2×D3×D411yescharacteristic
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C3×C4—22no—
677C3×C4—24no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23711yescharacteristic
687C3×C4C2×#23711yescharacteristic
688C3×C4C2×#23711yescharacteristic
689C3×C4C2×#23711yescharacteristic
690Dic3—41no—
691Dic3—41no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—122no—
705Dic3—122no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710C32#311911yescharacteristic, complemented, Sylow
711C23—21no—
712C23—61no—
713C23—61no—
714C23#381111yescharacteristic
715Q8—21no—
716Q8#380512yes—
717D4—24no—
718D4—21no—
719D4—61no—
720D4—61no—
721D4—61no—
722D4—61no—
723D4—241no—
724D4—241no—
725D4—721no—
726D4—721no—
727D4#380512yes—
728C2×C4—24no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—91no—
737C2×C4—91no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—721no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4#381111yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—61no—
748C8—61no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—44no—
756C2×C3—41no—
757C2×C3—42no—
758C2×C3—41no—
759C2×C3—42no—
760C2×C3—241no—
761C2×C3—241no—
762C2×C3#558611yescharacteristic
763C2×C3#558611yescharacteristic
764C2×C3#576911yescharacteristic
765C2×C3#577011yescharacteristic
766C2×C3#577411yescharacteristic
767C2×C3#577511yescharacteristic
768D3—81no—
769D3—81no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—22no—
774C22—41no—
775C22—41no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22C2×#381111yescharacteristic
783C4—21no—
784C4—22no—
785C4—121no—
786C4—121no—
787C4—181no—
788C4—181no—
789C4—181no—
790C4—181no—
791C4—361no—
792C4—361no—
793C4C2×#380511yescharacteristic
794C4C2×#380511yescharacteristic
795C3—21no—
796C3#8007211yescharacteristic, complemented
797C3#8007311yescharacteristic, complemented
798C2—41no—
799C2—42no—
800C2—241no—
801C2—241no—
802C2#1059546111yescharacteristic
803C2#1059546211yescharacteristic
804C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
2. #10595041C2semidirect
3. C3×#5238C2semidirect
4. C3×#5238C2semidirect
5. #10591622C2semidirect
6. #10591615C2semidirect
7. #10591572C2semidirect
8. #10591571C2semidirect
9. #10591486C2semidirect
10. #10591479C2semidirect
11. #10591436C2semidirect
12. #10591435C2semidirect
13. #10591094C2semidirect
14. #10591092C2semidirect
15. #10591062C2semidirect
68. #5238D3semidirect
69. #5238D3semidirect
710. C32#3119semidirect
796. C3#80072semidirect
797. C3#80073semidirect

Maximal subgroups

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

subgroupindex
#105962982
#105950412
C3×#52382
#105916222
#105916152
#105915722
#105915712
#105914862
#105914792
#105914362
#105914352
#105910942
#105910922
#105910622
#800733
#800723