Finite Group Databasebeta

← #11872140

Subgroups — #11872140

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#10596269C211yesmaximal, characteristic, complemented
2#10594984C211yesmaximal, characteristic, complemented
3C3×#5218C211yesmaximal, characteristic, complemented
4C3×#5217C211yesmaximal, characteristic
5#10591495C211yesmaximal, characteristic, complemented
6#10591494C211yesmaximal, characteristic, complemented
7#10591476C211yesmaximal, characteristic, complemented
8#10591476C211yesmaximal, characteristic, complemented
9#10591446C211yesmaximal, characteristic, complemented
10#10591445C211yesmaximal, characteristic, complemented
11#10591436C211yesmaximal, characteristic, complemented
12#10591435C211yesmaximal, characteristic, complemented
13#10591127C211yesmaximal, characteristic, complemented
14#10591093C211yesmaximal, characteristic, complemented
15#10591062C211yesmaximal, characteristic, complemented
16#80136—31nomaximal
17#79992—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C2×#3757—21no—
20C2×#3757—21no—
21D4×C3⋊Dic3—21no—
22D4×C3⋊Dic3—21no—
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26D4×C3⋊Dic3C2211yescharacteristic
27#64135C2211yescharacteristic
28#64135C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#924C2211yescharacteristic
35#63969—21no—
36#63959—21no—
37#63919C2211yescharacteristic, complemented
38#63898C2211yescharacteristic, complemented
39#63893—21no—
40#63863C2211yescharacteristic, complemented
41#63861—21no—
42#63843C2211yescharacteristic, complemented
43C3×#832C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63575C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63555C2211yescharacteristic, complemented
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5798—31no—
63#5798—61no—
64#5643—31no—
65#5603—31no—
66C3×#450—31no—
67C3×#447—31no—
68#5218D311yescharacteristic, complemented
69#5217D311yescharacteristic
70#5165—31no—
71#5165—31no—
72#5164—31no—
73Dic3×SD16—31no—
74#5153—31no—
75#5153—31no—
76#5152—31no—
77Dic3×D8—31no—
78#5045—31no—
79#5035—31no—
80#4785—31no—
81#4761—31no—
82#4761—31no—
83#4759—31no—
84#4759—31no—
85#4758—31no—
86#4757—31no—
87#4756—31no—
88#4737—31no—
89#4723—31no—
90#4720—31no—
91#4720—31no—
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C22×C3⋊Dic3—21no—
101C22×C3⋊Dic3—21no—
102C22×C3⋊Dic3—21no—
103C2×C3×#67—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×D3×Dic3—21no—
108#3757—21no—
109#3757—21no—
110#3757—21no—
111#3757—21no—
112#3757—21no—
113#3757D411yescharacteristic
114#3757D411yescharacteristic
115C4⋊(C3⋊Dic3)D411yescharacteristic
116C4⋊(C3⋊Dic3)D411yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C3×#217—21no—
123C3×#214—22no—
124C3×#214—22no—
125C3×#213—22no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3118—91noSylow
142C22×C3×D4—21no—
143C22×C3×D4C2×D311yescharacteristic
144C22×C3×D4C2×D311yescharacteristic
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C2×C3×D8—31no—
149C3×C22⋊Q8—31no—
150C3×#121—31no—
151C2×#217—61no—
152C2×#217—61no—
153C2×#217—61no—
154C2×#217—61no—
155C2×#217—62no—
156C2×#217—62no—
157#947—31no—
158Q8×Dic3—31no—
159#936—31no—
160#936—61no—
161#935—61no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—31no—
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—61no—
178D4×Dic3—61no—
179D4×Dic3—62no—
180D4×Dic3—62no—
181C2×#214C2×D311yescharacteristic
182C2×#214C2×D311yescharacteristic
183C2×#213C2×D311yescharacteristic
184C2×#213C2×D311yescharacteristic
185#930C2×D311yescharacteristic
186#926—31no—
187#926—31no—
188#926—31no—
189#926—31no—
190#926—61no—
191#926—61no—
192#924C2×D311yescharacteristic
193#898—61no—
194#897—61no—
195#893—31no—
196#888—31no—
197#888—31no—
198#887—31no—
199#885—61no—
200#883—61no—
201#879—61no—
202#878—61no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830C2×D311yescharacteristic
218#830C2×D311yescharacteristic
219#821—31no—
220#821—31no—
221#818—31no—
222#818—31no—
223#817—31no—
224#817—31no—
225#816—31no—
226#816—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—24no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—81no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×D4—24no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4#4112yes—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—81no—
258C2×C3⋊Dic3—81no—
259C2×C3⋊Dic3—81no—
260C2×C3⋊Dic3—81no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
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—91no—
282#482—91no—
283#476—91no—
284#474—91no—
285#463—91no—
286#463—91no—
287#450—31no—
288#447—31no—
289#442—91no—
290#440—91no—
291C4×SD16—91no—
292C4×D8—91no—
293#433—91no—
294C24×C3—22no—
295C24×C3—21no—
296C24×C3—21no—
297C2×C3×Q8—31no—
298C2×C3×D4—22no—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—22no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C22×D311yescharacteristic
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—62no—
329C22×Dic3—62no—
330C22×Dic3—62no—
331C22×Dic3—62no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—62no—
338C3×SD16—62no—
339C3×D8—62no—
340C3×D8—62no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—21no—
351#217—31no—
352#217—31no—
353#217—31no—
354#217—31no—
355#217—61no—
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—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—62no—
369#217—62no—
370#217—62no—
371#217—62no—
372#217—62no—
373#217—61no—
374#217—61no—
375#214—22no—
376#214—22no—
377#213—22no—
378#213—22no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—31no—
405C4×Dic3—31no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—62no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—84no—
427C22×C32C22×D411yescharacteristic
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C32×C4—21no—
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—
442C3×Dic3—41no—
443C22×D4D3211yescharacteristic
444C2×SD16—31no—
445C2×SD16—31no—
446C2×D8—31no—
447C2×D8—31no—
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#117—91no—
466C2×C22⋊C4—181no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471#106—91no—
472C4⋊C8—91no—
473C4⋊C8—91no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484#97—91no—
485C4×C8—91no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—28no—
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—61no—
497C23×C3—81no—
498C23×C3—81no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3—82no—
502C23×C3—82no—
503C23×C3D3×D411yescharacteristic
504C23×C3D3×D411yescharacteristic
505C22×D3—21no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×D4—28no—
509C3×D4—24no—
510C3×D4—24no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—22no—
518C3×D4—22no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—241no—
522C3×D4#23712yes—
523C3×D4#23712yes—
524C3×D4#23712yes—
525C3×D4#23712yes—
526C2×C3×C4—22no—
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—21no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—81no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3—241no—
567C2×Dic3—241no—
568C2×Dic3—241no—
569C2×Dic3—241no—
570C2×Dic3—241no—
571C2×Dic3—241no—
572C2×Dic3—242no—
573C2×Dic3—242no—
574C2×Dic3—242no—
575C2×Dic3—242no—
576D12—21no—
577D12—21no—
578C4×D3—241no—
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—42no—
593C2×C32—42no—
594C2×C32#52511yescharacteristic
595C2×C32#57611yescharacteristic
596C2×C32#57711yescharacteristic
597C3×D3—81no—
598C24—21no—
599C2×Q8—31no—
600C2×Q8—181no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—21no—
604C2×D4—31no—
605C2×D4—61no—
606C2×D4C2×D3211yescharacteristic
607C2×D4C2×D3211yescharacteristic
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—62no—
615SD16—62no—
616D8—62no—
617D8—62no—
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—91no—
628C4⋊C4—91no—
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—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—91no—
644C42—91no—
645C42—181no—
646C42—181no—
647C22×C3—22no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—88no—
676C22×C3—84no—
677C22×C3—84no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C3×C4—22no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4C2×#23711yescharacteristic
695C3×C4C2×#23711yescharacteristic
696C3×C4C2×#23711yescharacteristic
697C3×C4C2×#23711yescharacteristic
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—61no—
707Dic3—61no—
708Dic3—61no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—121no—
713Dic3—122no—
714Dic3—122no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719C32#311811yescharacteristic, complemented, Sylow
720C23—24no—
721C23—21no—
722C23—21no—
723C23—61no—
724C23—81no—
725C23—81no—
726C23#381111yescharacteristic
727Q8—61no—
728Q8—61no—
729Q8—721no—
730D4—24no—
731D4—21no—
732D4—21no—
733D4—61no—
734D4—61no—
735D4—241no—
736D4#380512yes—
737D4#380512yes—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—91no—
746C2×C4—91no—
747C2×C4—181no—
748C2×C4—181no—
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—44no—
765C2×C3—44no—
766C2×C3—41no—
767C2×C3—42no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—42no—
771C2×C3—42no—
772C2×C3—241no—
773C2×C3#558611yescharacteristic
774C2×C3#558611yescharacteristic
775C2×C3#575711yescharacteristic
776C2×C3#576211yescharacteristic
777C2×C3#577411yescharacteristic
778C2×C3#577511yescharacteristic
779D3—81no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—22no—
784C22—22no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—84no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22C2×#381111yescharacteristic
794C4—21no—
795C4—121no—
796C4—121no—
797C4—121no—
798C4—181no—
799C4—181no—
800C4—181no—
801C4—181no—
802C4—361no—
803C4—361no—
804C4C2×#380511yescharacteristic
805C4C2×#380511yescharacteristic
806C3—21no—
807C3#7999211yescharacteristic, complemented
808C3#8013611yescharacteristic, complemented
809C2—41no—
810C2—42no—
811C2—42no—
812C2—241no—
813C2#1059510211yescharacteristic
814C2#1059511511yescharacteristic
815C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×#5217C2
hypercenterC22×D4D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #10596269C2semidirect
2. #10594984C2semidirect
3. C3×#5218C2semidirect
5. #10591495C2semidirect
6. #10591494C2semidirect
7. #10591476C2semidirect
8. #10591476C2semidirect
9. #10591446C2semidirect
10. #10591445C2semidirect
11. #10591436C2semidirect
12. #10591435C2semidirect
13. #10591127C2semidirect
14. #10591093C2semidirect
15. #10591062C2semidirect
37. #63919C22semidirect
38. #63898C22semidirect
40. #63863C22semidirect
42. #63843C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
59. #63555C22semidirect
60. #63553C22semidirect
68. #5218D3semidirect
719. C32#3118semidirect
807. C3#79992semidirect
808. C3#80136semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105949842
C3×#52182
C3×#52172
#105914952
#105914942
#105914762
#105914462
#105914452
#105914362
#105914352
#105911272
#105910932
#105910622
#801363
#799923