Finite Group Databasebeta

← #11878505

Subgroups — #11878505

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic, complemented
2#10594894C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5#10591657C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591521C211yesmaximal, characteristic, complemented
10#10591502C211yesmaximal, characteristic, complemented
11#10591449C211yesmaximal, characteristic, complemented
12#10591413C211yesmaximal, characteristic, complemented
13#10591145C211yesmaximal, characteristic, complemented
14#10591133C211yesmaximal, characteristic, complemented
15#10591132C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#80239—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23#64139C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#939—21no—
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#930—21no—
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C3×#924—21no—
35C3×#924C2211yescharacteristic
36#63971—21no—
37#63958—21no—
38#63909C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63888—21no—
41#63886—21no—
42#63856C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63657C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5833D311yescharacteristic, complemented
64#5629—31no—
65C3×#452—31no—
66#5239D311yescharacteristic, complemented
67#5238—31no—
68#5238—31no—
69#5238—61no—
70#5234—31no—
71#5188—31no—
72#5187—31no—
73#5174—31no—
74#5172—31no—
75#5051—31no—
76#5049—31no—
77#5047—31no—
78#5044—31no—
79#5044—31no—
80#5042—31no—
81#5038—31no—
82#5037—31no—
83#5033—31no—
84#4970—31no—
85#4967—31no—
86#4812—31no—
87#4811—31no—
88#4775—31no—
89#4774—31no—
90#4736—31no—
91#4727—31no—
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12D411yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6D411yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117#3799—41no—
118#3799—41no—
119#3755—41no—
120#3753—41no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#216—41no—
129C3×#214—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3724—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3203—91noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41C2×D311yescharacteristic
151C2×C3×#41C2×D311yescharacteristic
152C2×#239—31no—
153C2×#235—31no—
154C2×#235C2×D311yescharacteristic
155C2×C3×Q16—31no—
156C2×C3×SD16—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×#121—61no—
165C3×#121—61no—
166C2×C3×C4⋊C4—31no—
167#946—31no—
168#946—61no—
169#946C2×D311yescharacteristic
170#946C2×D311yescharacteristic
171C2×#216C2×D311yescharacteristic
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175#939—21no—
176#939—21no—
177#939—61no—
178#939—61no—
179#938—61no—
180#938C2×D311yescharacteristic
181#938C2×D311yescharacteristic
182C2×#214C2×D311yescharacteristic
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—61no—
186#930—21no—
187#930—31no—
188#930—31no—
189#930—31no—
190#930—61no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3C2×D311yescharacteristic
193#924—21no—
194#924—31no—
195#924C2×D311yescharacteristic
196C2×#208—31no—
197C22×C3⋊C8—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×D3×C8—31no—
200#896—61no—
201#895—31no—
202#895—61no—
203D3×C4⋊C4—31no—
204#884—61no—
205#884—61no—
206C3×#103—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#832—31no—
216#832—31no—
217#832—61no—
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—61no—
224#830C2×D311yescharacteristic
225#821—31no—
226#821—31no—
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8—31no—
229#818—31no—
230#818—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240#807—31no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—42no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257#638—81no—
258C2×C3⋊Dic3—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—81no—
264C3×#67—81no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—81no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—41no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—41no—
280#626—42no—
281#626—81no—
282#624—42no—
283D3×Dic3—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—31no—
299#452—91no—
300#449—91no—
301#449—91no—
302#408—91no—
303C3×#41—41no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—42no—
308C3×#41—42no—
309C3×#41—121no—
310C3×#41—121no—
311C2×C3×Q8—21no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—41no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—41no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C2×#67#6711yescharacteristic
344C2×#67#6711yescharacteristic
345C22×Dic3—21no—
346C22×Dic3—61no—
347#239—121no—
348#239—121no—
349#235—41no—
350#235—41no—
351#235—121no—
352#235—121no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12#6711yescharacteristic
359C2×C4×D3—61no—
360C2×C4×D3—61no—
361C2×C4×D3—61no—
362C2×C4×D3C22×D311yescharacteristic
363C2×C4×D3C22×D311yescharacteristic
364C2×Dic6#6711yescharacteristic
365C2×Dic6C22×D311yescharacteristic
366C3×Q16—121no—
367C3×SD16—121no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382#217—21no—
383#217—21no—
384#217—21no—
385#217—61no—
386#216—41no—
387#215—121no—
388#215—121no—
389#215—122no—
390#214—41no—
391#213—121no—
392#213—121no—
393#213—122no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—121no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416#208—121no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—121no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426ΓL(1,𝔽25)—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3—41no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4H(5,𝔽2)11yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—41no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—91no—
457C2×#41D3211yescharacteristic
458C2×Q16—31no—
459C2×SD16—31no—
460C2×SD16—91no—
461C2×D8—91no—
462C2×M16—91no—
463C22×C8—91no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—31no—
467C22⋊Q8—61no—
468C22⋊Q8—91no—
469C22⋊Q8—181no—
470#121—31no—
471#121—31no—
472#121—61no—
473#121—61no—
474#121—61no—
475#121—91no—
476#121—91no—
477#121—181no—
478#121—181no—
479#121—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—91no—
483#107—91no—
484#107—91no—
485#107—91no—
486#103—31no—
487#103—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494C22⋊C8—31no—
495C22⋊C8—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3D3×D411yescharacteristic
505C23×C3C2×#6711yescharacteristic
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—121no—
509C22×D3C2×#6711yescharacteristic
510C22×D3C2×#6711yescharacteristic
511C3×Q8—22no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—41no—
517C3×Q8—61no—
518C3×Q8—61no—
519C3×Q8—121no—
520C3×D4—22no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—41no—
526C3×D4—42no—
527C3×D4—42no—
528C3×D4—44no—
529C3×D4—121no—
530C3×D4—121no—
531C3×D4—121no—
532C3×D4—241no—
533C3×D4—241no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—44no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—241no—
559C2×C3×C4D3×D411yescharacteristic
560C2×C3×C4C2×#6711yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C23×D311yescharacteristic
563#67—41no—
564#67—41no—
565#67—81no—
566#67—81no—
567#67—122no—
568#67—241no—
569#67—241no—
570#67—241no—
571#67—242no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—81no—
579C2×Dic3—121no—
580C2×Dic3—241no—
581C2×Dic3C2×#6711yescharacteristic
582C2×Dic3C2×#6711yescharacteristic
583D12—41no—
584D12—61no—
585D12—61no—
586D12—61no—
587D12—61no—
588D12—121no—
589D12—121no—
590D12—122no—
591D12—241no—
592C4×D3—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—21no—
596C4×D3—122no—
597C4×D3—122no—
598C4×D3—241no—
599Dic6—21no—
600Dic6—21no—
601Dic6—41no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—121no—
611C3⋊C8—121no—
612C2×C32—41no—
613C2×C32—81no—
614C2×C32#53411yescharacteristic
615C2×C32#57611yescharacteristic
616C2×C32#57811yescharacteristic
617C3⋊D3—81no—
618C3×D3—41no—
619C3×D3—41no—
620#41—41no—
621#41—41no—
622#41—121no—
623#41—121no—
624#41—361no—
625#41—361no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8C2×D3211yescharacteristic
629C2×D4—21no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—91no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4—181no—
639C2×D4C2×D3211yescharacteristic
640C22×C4—21no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—181no—
645C22×C4—181no—
646C22×C4C2×D3211yescharacteristic
647Q16—121no—
648SD16—121no—
649SD16—361no—
650D8—361no—
651M16—361no—
652C2×C8—31no—
653C2×C8—31no—
654C2×C8—91no—
655C2×C8—91no—
656C2×C8—361no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—31no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—181no—
666C4⋊C4—181no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22⋊C4—181no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C22×#6711yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3—121no—
714C2×D3—241no—
715C2×D3—241no—
716C2×D3—241no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—61no—
726C3×C4—61no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4#100411yescharacteristic
732C3×C4#100411yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4#100411yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741Dic3—121no—
742Dic3—121no—
743Dic3—241no—
744C32#320311yescharacteristic, complemented, Sylow
745C23—21no—
746C23—31no—
747C23—31no—
748C23—181no—
749C23D3×#6711yescharacteristic
750Q8—21no—
751Q8—21no—
752Q8—61no—
753Q8—61no—
754Q8—121no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—121no—
759D4—121no—
760D4—121no—
761D4—181no—
762D4—181no—
763D4—241no—
764D4—241no—
765D4—362no—
766D4—721no—
767D4—721no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—42no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—181no—
783C2×C4—241no—
784C2×C4—362no—
785C2×C4—721no—
786C2×C4D3×#6711yescharacteristic
787C2×C4C22×D3211yescharacteristic
788C8—61no—
789C8—61no—
790C8—181no—
791C8—181no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—41no—
796C2×C3—41no—
797C2×C3—81no—
798C2×C3—82no—
799C2×C3—81no—
800C2×C3—81no—
801C2×C3—121no—
802C2×C3—121no—
803C2×C3#558911yescharacteristic
804C2×C3#576911yescharacteristic
805C2×C3#577911yescharacteristic
806C2×C3#580411yescharacteristic
807C2×C3#583511yescharacteristic
808C2×C3#583811yescharacteristic
809D3—41no—
810D3—41no—
811D3—241no—
812D3—241no—
813D3—481no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—361no—
827C22—361no—
828C22—361no—
829C22C2×D3×#6711yescharacteristic
830C4—21no—
831C4—41no—
832C4—61no—
833C4—61no—
834C4—121no—
835C4—121no—
836C4—121no—
837C4—121no—
838C4—361no—
839C4#6433011yescharacteristic
840C4#6433011yescharacteristic
841C3—21no—
842C3#8023911yescharacteristic, complemented
843C3#8342611yescharacteristic, complemented
844C2—41no—
845C2—81no—
846C2—121no—
847C2—121no—
848C2—721no—
849C2#1059545611yescharacteristic
850C2#1059546511yescharacteristic
851C2#1059552411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3203
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. C3×#5833C2semidirect
2. #10594894C2semidirect
3. #10592937C2semidirect
4. C3×#5239C2semidirect
5. #10591657C2semidirect
6. #10591635C2semidirect
7. #10591589C2semidirect
8. #10591551C2semidirect
9. #10591521C2semidirect
10. #10591502C2semidirect
11. #10591449C2semidirect
12. #10591413C2semidirect
13. #10591145C2semidirect
14. #10591133C2semidirect
15. #10591132C2semidirect
63. #5833D3semidirect
66. #5239D3semidirect
744. C32#3203semidirect
842. C3#80239semidirect
843. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
#105948942
#105929372
C3×#52392
#105916572
#105916352
#105915892
#105915512
#105915212
#105915022
#105914492
#105914132
#105911452
#105911332
#105911322
#834263
#802393