Finite Group Databasebeta

← #11878502

Subgroups — #11878502

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5608C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic, complemented
3#10592732C211yesmaximal, characteristic, complemented
4C3×#5037C211yesmaximal, characteristic, complemented
5#10591502C211yesmaximal, characteristic, complemented
6#10591498C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10591170C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic, complemented
11#10591103C211yesmaximal, characteristic, complemented
12#10590518C211yesmaximal, characteristic, complemented
13#10590517C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590498C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#80095—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#939—21no—
24C3×#938—21no—
25C3×#938C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#897C2211yescharacteristic
30C3×D3×C4⋊C4C2211yescharacteristic
31C3×#884—21no—
32C3×#878—21no—
33#63980—21no—
34#63980—21no—
35#63908—21no—
36#63908C2211yescharacteristic
37#63908C2211yescharacteristic
38#63856—21no—
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63657C2211yescharacteristic
48#63634C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5833—31no—
64#5608D311yescharacteristic, complemented
65C3×#449—31no—
66#5239—31no—
67#5239—31no—
68#5238—31no—
69#5234—31no—
70#5174—31no—
71#5173—31no—
72#5158—31no—
73#5157—31no—
74#5051—31no—
75#5049—31no—
76#5047—31no—
77#5044—31no—
78#5042—31no—
79#5038—31no—
80#5037D311yescharacteristic, complemented
81#5033—31no—
82#5033—31no—
83#5033—61no—
84#4970—31no—
85#4967—31no—
86#4813—31no—
87#4811—31no—
88#4780—31no—
89#4774—31no—
90#4727—31no—
91#4722—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C3×#237—41no—
103C3×#237—41no—
104C3×#235—41no—
105C3×#235—41no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6D411yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#625—21no—
118C2×#625—21no—
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#214—41no—
129C3×#213—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138#3724—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3718—41no—
144#3715—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3203—91noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×#237C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×SD16—31no—
155C2×C3×D8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×#121—21no—
160C3×#121—31no—
161C3×#121—61no—
162C3×#121—61no—
163C3×#121—61no—
164C3×#121C2×D311yescharacteristic
165C3×#121C2×D311yescharacteristic
166C2×C3×C4⋊C4—31no—
167#946—31no—
168#946—31no—
169#946—61no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#215—31no—
173#939—21no—
174#939—61no—
175#939—61no—
176#939—61no—
177#939—61no—
178#938—21no—
179#938—31no—
180#938—31no—
181#938—61no—
182#938C2×D311yescharacteristic
183C2×#214—31no—
184C2×#214C2×D311yescharacteristic
185C2×#213C2×D311yescharacteristic
186#930—31no—
187#930—31no—
188#930—61no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192#924—31no—
193#924—31no—
194#924—61no—
195#924C2×D311yescharacteristic
196C2×#208—31no—
197C22×C3⋊C8—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×D3×C8—31no—
200#897C2×D311yescharacteristic
201D3×C4⋊C4C2×D311yescharacteristic
202#884—21no—
203#878—21no—
204C3×#103—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832—61no—
217#830—31no—
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#818—31no—
227#816—31no—
228#816—31no—
229#810—31no—
230#810C2×D311yescharacteristic
231#809—31no—
232#809C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807—61no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
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—
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—41no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—42no—
276C3×C4×D3—81no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—41no—
282#625—81no—
283#625—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#484—91no—
291#484—91no—
292#480—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—91no—
299#452—91no—
300#449—31no—
301#449—91no—
302#408—91no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C3×#41—121no—
308C3×#41—121no—
309C2×C3×Q8—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—41no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67#6711yescharacteristic
341C2×#67#6711yescharacteristic
342C22×Dic3—21no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3—121no—
346#237—41no—
347#237—41no—
348#235—41no—
349#235—41no—
350#235—41no—
351#235—41no—
352C2×D12#6711yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3C22×D311yescharacteristic
357C2×C4×D3C22×D311yescharacteristic
358C2×Dic6#6711yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—121no—
362C3×D8—121no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—41no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378#217—21no—
379#217—21no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#216—121no—
385#216—121no—
386#215—121no—
387#214—41no—
388#214—121no—
389#213—41no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395C4⋊Dic3—21no—
396C4⋊Dic3—31no—
397C4⋊Dic3—31no—
398C4⋊Dic3—31no—
399C4⋊Dic3—31no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404C4⋊Dic3—121no—
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412#208—121no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—31no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—61no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422ΓL(1,𝔽25)—121no—
423D3×C8—121no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C22×D411yescharacteristic
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4—41no—
442C32×C4H(5,𝔽2)11yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—31no—
454C2×Q16—91no—
455C2×SD16—31no—
456C2×SD16—91no—
457C2×D8—31no—
458C2×M16—91no—
459C22×C8—91no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—61no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—181no—
466#121—31no—
467#121—61no—
468#121—61no—
469#121—61no—
470#121—91no—
471#121—91no—
472#121—181no—
473#121—181no—
474#121—181no—
475#121D3211yescharacteristic
476C2×C4⋊C4—31no—
477C2×C4⋊C4—91no—
478#107—91no—
479#107—91no—
480#107—91no—
481#107—91no—
482#103—31no—
483#103—91no—
484#103—91no—
485#103—91no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3—31no—
499C23×C3—41no—
500C23×C3—61no—
501C23×C3D3×D411yescharacteristic
502C23×C3C2×#6711yescharacteristic
503C22×D3—21no—
504C22×D3C2×#6711yescharacteristic
505C22×D3C2×#6711yescharacteristic
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8—121no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—81no—
520C3×D4—81no—
521C3×D4—82no—
522C3×D4—121no—
523C3×D4—121no—
524C3×D4—121no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
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—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4—122no—
550C2×C3×C4—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—41no—
556#67—41no—
557#67—42no—
558#67—42no—
559#67—81no—
560#67—241no—
561#67—241no—
562#67—241no—
563#67—241no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—42no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—241no—
575C2×Dic3—241no—
576C2×Dic3—242no—
577C2×Dic3C2×#6711yescharacteristic
578C2×Dic3C2×#6711yescharacteristic
579D12—21no—
580D12—21no—
581D12—41no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—42no—
587C4×D3—81no—
588Dic6—21no—
589Dic6—21no—
590Dic6—21no—
591Dic6—21no—
592Dic6—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C3⋊C8—61no—
598C3⋊C8—61no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C3⋊C8—121no—
603C2×C32—41no—
604C2×C32—81no—
605C2×C32#53411yescharacteristic
606C2×C32#57611yescharacteristic
607C2×C32#57811yescharacteristic
608C3×D3—41no—
609C3×D3—41no—
610C3×D3—81no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—121no—
615#41—121no—
616#41—121no—
617C2×Q8—31no—
618C2×Q8—31no—
619C2×Q8—31no—
620C2×D4—21no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—31no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4C2×D3211yescharacteristic
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—181no—
637C22×C4C2×D3211yescharacteristic
638Q16—361no—
639SD16—121no—
640SD16—361no—
641D8—121no—
642M16—361no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—91no—
646C2×C8—91no—
647C2×C8—361no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—91no—
653C4⋊C4—91no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C4⋊C4C2×D3211yescharacteristic
658C22⋊C4—21no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C22×#6711yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—81no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4#100411yescharacteristic
719C3×C4#100411yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4#100411yescharacteristic
722Dic3—21no—
723Dic3—21no—
724Dic3—41no—
725Dic3—41no—
726Dic3—41no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732Dic3—241no—
733C32#320311yescharacteristic, complemented, Sylow
734C23—21no—
735C23—31no—
736C23—31no—
737C23—61no—
738C23D3×#6711yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—61no—
743Q8—121no—
744D4—21no—
745D4—21no—
746D4—61no—
747D4—61no—
748D4—81no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—122no—
753D4—122no—
754D4—241no—
755D4—721no—
756D4—721no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—122no—
770C2×C4—122no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—241no—
774C2×C4—721no—
775C2×C4D3×#6711yescharacteristic
776C2×C4C22×D3211yescharacteristic
777C8—61no—
778C8—61no—
779C8—181no—
780C8—181no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—42no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—81no—
788C2×C3—81no—
789C2×C3—121no—
790C2×C3—121no—
791C2×C3—161no—
792C2×C3—241no—
793C2×C3#558911yescharacteristic
794C2×C3#577111yescharacteristic
795C2×C3#577411yescharacteristic
796C2×C3#580411yescharacteristic
797C2×C3#583511yescharacteristic
798C2×C3#583811yescharacteristic
799D3—41no—
800D3—41no—
801D3—81no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22C2×D3×#6711yescharacteristic
818C4—21no—
819C4—41no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—361no—
826C4—361no—
827C4#6431311yescharacteristic
828C4#6431311yescharacteristic
829C3—21no—
830C3#8009511yescharacteristic, complemented
831C3#8342611yescharacteristic, complemented
832C2—41no—
833C2—81no—
834C2—121no—
835C2—121no—
836C2—241no—
837C2#1059509711yescharacteristic
838C2#1059523011yescharacteristic
839C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5608C2semidirect
2. #10595044C2semidirect
3. #10592732C2semidirect
4. C3×#5037C2semidirect
5. #10591502C2semidirect
6. #10591498C2semidirect
7. #10591461C2semidirect
8. #10591450C2semidirect
9. #10591170C2semidirect
10. #10591145C2semidirect
11. #10591103C2semidirect
12. #10590518C2semidirect
13. #10590517C2semidirect
14. #10590503C2semidirect
15. #10590498C2semidirect
64. #5608D3semidirect
80. #5037D3semidirect
733. C32#3203semidirect
830. C3#80095semidirect
831. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#56082
#105950442
#105927322
C3×#50372
#105915022
#105914982
#105914612
#105914502
#105911702
#105911452
#105911032
#105905182
#105905172
#105905032
#105904982
#834263
#800953