Finite Group Databasebeta

← #11810262

Subgroups — #11810262

Order 1152.

1413 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63904C211yesmaximal, characteristic
2C2×#63895C211yesmaximal, characteristic, complemented
3C2×#63883C211yesmaximal, characteristic, complemented
4C2×#63851C211yesmaximal, characteristic, complemented
5#10592366C211yesmaximal, characteristic, complemented
6C3×#4667C211yesmaximal, characteristic, complemented
7C3×#4657C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic
9#10591367C211yesmaximal, characteristic, complemented
10#10591340C211yesmaximal, characteristic, complemented
11#10591308C211yesmaximal, characteristic, complemented
12#10591306C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic
14#10591235C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16#77742—31nomaximal
17#73888—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63904—24no—
46#63895—24no—
47#63883—24no—
48#63851—24no—
49C32×#95C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C4×#67—31no—
58C2×#924—31no—
59C2×#897—31no—
60C2×#896—31no—
61C2×#896—31no—
62C2×#893—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C3×#398—31no—
66C3×#380—31no—
67#4994—31no—
68#4994—31no—
69#4987—31no—
70#4982—31no—
71#4973—31no—
72#4972—31no—
73#4956—31no—
74#4956—31no—
75#4948—31no—
76#4948—31no—
77#4667—31no—
78#4667—31no—
79#4667—31no—
80#4667—61no—
81#4667D311yescharacteristic, complemented
82#4665—31no—
83#4665—31no—
84#4657—31no—
85#4657D311yescharacteristic, complemented
86#4647—31no—
87#4646—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—41no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×#627—22no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626Q814yescomplemented
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—41no—
120C2×#624D414yes—
121#3752—22no—
122#3752—22no—
123#3750—22no—
124#3750—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×C4⋊Dic3—22no—
128C3×Dic3⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—41no—
136Dic3⋊Dic3D414yescomplemented
137#3722—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141Dic32—22no—
142#2417—91noSylow
143C23×C3×C4—31no—
144C22×#67—31no—
145C22×D12—31no—
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3—61no—
153C22×C4×D3C2×D311yescharacteristic
154C22×Dic6—31no—
155C22×Dic6—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C4×#67—64no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4—61no—
179C2×(C2×D3)⋊C4C2×D311yescharacteristic
180C2×(C2×D3)⋊C4C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3C2×D311yescharacteristic
186#924—64no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—61no—
196C2×Dic3⋊C4—61no—
197C2×Dic3⋊C4C2×D311yescharacteristic
198C2×Dic3⋊C4C2×D311yescharacteristic
199C2×Dic3⋊C4C2×D311yescharacteristic
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204#897—64no—
205#896—64no—
206#896—64no—
207#893—64no—
208D3×C4⋊C4—64no—
209D3×C4⋊C4—64no—
210C3×#95—21no—
211C3×#95—31no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95C2×D311yescharacteristic
215C3×#95C2×D311yescharacteristic
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—61no—
225C3⋊#95C2×D311yescharacteristic
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C23×C32C2411yescharacteristic
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3C2×D412yes—
234C22×C3⋊D3C2×Q812yes—
235C22×C3⋊D3#4112yes—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×Q812yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3C2×D412yes—
261C4×C3⋊D3—44no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D412yes—
278C2×C3×Dic3C2×D412yes—
279C2×C3×Dic3C2×D412yes—
280C2×C3×Dic3C2×D412yes—
281C2×C3×Dic3C2×Q812yes—
282C2×C3×Dic3#4112yes—
283C3×C4×D3—44no—
284#627—44no—
285#626—28no—
286#624—28no—
287#624—44no—
288C2×C22⋊Q8—91no—
289C2×C22⋊Q8—91no—
290C2×C4×D4—91no—
291C22×C4⋊C4—91no—
292#398—31no—
293#398—91no—
294#396—91no—
295#396—91no—
296#391—91no—
297#389—91no—
298#386—91no—
299#386—91no—
300#380—31no—
301#380—91no—
302#380—91no—
303C24×C3—31no—
304C23×D3—31no—
305C23×D3—31no—
306C23×D3—61no—
307C23×D3C22×D311yescharacteristic
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—62no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—34no—
328C2×#67—62no—
329C2×#67—62no—
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C2×D12—34no—
347C2×D12—62no—
348C2×D12—62no—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3—62no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—64no—
366C2×C4×D3—62no—
367C2×C4×D3—122no—
368C2×C4×D3—121no—
369C2×C4×D3—121no—
370C2×C4×D3—121no—
371C2×C4×D3—121no—
372C2×C4×D3—122no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C3×C4⋊C4—62no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—62no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C22⋊C4—121no—
386C3×C22⋊C4—121no—
387#217—62no—
388#217—62no—
389#217—62no—
390(C2×D3)⋊C4—41no—
391(C2×D3)⋊C4—41no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—62no—
394(C2×D3)⋊C4—62no—
395(C2×D3)⋊C4—62no—
396(C2×D3)⋊C4—62no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—122no—
402(C2×D3)⋊C4—122no—
403C4⋊Dic3—22no—
404C4⋊Dic3—34no—
405C4⋊Dic3—62no—
406C4⋊Dic3—62no—
407C4⋊Dic3—121no—
408Dic3⋊C4—22no—
409Dic3⋊C4—22no—
410Dic3⋊C4—22no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—34no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—122no—
419Dic3⋊C4—121no—
420Dic3⋊C4—121no—
421Dic3⋊C4—121no—
422Dic3⋊C4—122no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C22×C32C22×D411yescharacteristic
426C22×C32C22×D411yescharacteristic
427C22×C32C22×Q811yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32H(5,𝔽2)11yescharacteristic
431C22×C322−1+411yescharacteristic
432C2×C3⋊D3—22no—
433C2×C3⋊D3—22no—
434C2×C3⋊D3—22no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3—22no—
438C2×C3⋊D3C22⋊Q814yescomplemented
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—41no—
449C3⋊Dic3—22no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3#12114yes—
459C22×Q8—91no—
460C22×D4—91no—
461C23×C4—31no—
462C23×C4—91no—
463C23×C4—91no—
464C23×C4—91no—
465C22⋊Q8—184no—
466C22⋊Q8—184no—
467C4×D4—184no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—31no—
471C2×C4⋊C4—31no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—31no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—184no—
481C2×C22⋊C4—31no—
482C2×C22⋊C4—31no—
483C2×C22⋊C4—91no—
484C2×C22⋊C4—91no—
485C2×C22⋊C4—91no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—91no—
488C2×C22⋊C4—91no—
489C2×C42—91no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95—91no—
497#95D3211yescharacteristic
498C23×C3—21no—
499C23×C3—32no—
500C23×C3—61no—
501C23×C3—61no—
502C23×C3—61no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3C23×D311yescharacteristic
507C23×C3C23×D311yescharacteristic
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—32no—
515C22×D3—32no—
516C22×D3—32no—
517C22×D3—32no—
518C22×D3—32no—
519C22×D3—32no—
520C22×D3—62no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—61no—
527C22×D3—61no—
528C22×D3—61no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—121no—
533C22×D3—121no—
534C22×D3—121no—
535C22×D3D3×Q812yes—
536C2×C3×C4—22no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—124no—
585#67—68no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—121no—
627C2×Dic3—121no—
628C2×Dic3#23512yes—
629C2×Dic3D3×D412yes—
630C2×Dic3D3×D412yes—
631C2×Dic3D3×D412yes—
632C2×Dic3D3×D412yes—
633C2×Dic3D3×Q812yes—
634D12—68no—
635C4×D3—44no—
636C4×D3—68no—
637C4×D3—68no—
638C4×D3—124no—
639C4×D3—124no—
640C4×D3—124no—
641C4×D3—124no—
642C4×D3—128no—
643Dic6—124no—
644Dic6—124no—
645C2×C32C2×#12111yescharacteristic
646C2×C32C2×C22⋊Q811yescharacteristic
647C2×C32#53711yescharacteristic
648C2×C32#54611yescharacteristic
649C2×C32D4×Q811yescharacteristic
650C2×C32#55211yescharacteristic
651C2×C32#55411yescharacteristic
652C3⋊D3—24no—
653C3×D3—42no—
654C24—31no—
655C24—91no—
656C2×Q8—182no—
657C2×Q8—182no—
658C2×Q8—182no—
659C2×D4—94no—
660C2×D4—182no—
661C2×D4—182no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4—94no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—91no—
676C22×C4—182no—
677C22×C4—182no—
678C22×C4—182no—
679C22×C4—182no—
680C22×C4—182no—
681C22×C4—182no—
682C22×C4—361no—
683C22×C4—361no—
684C22×C4C2×D3211yescharacteristic
685C22×C4C2×D3211yescharacteristic
686C22×C4C2×D3211yescharacteristic
687C4⋊C4—62no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—62no—
691C4⋊C4—62no—
692C4⋊C4—62no—
693C4⋊C4—94no—
694C4⋊C4—182no—
695C4⋊C4—182no—
696C4⋊C4—182no—
697C4⋊C4—361no—
698C4⋊C4—361no—
699C22⋊C4—121no—
700C22⋊C4—121no—
701C22⋊C4—182no—
702C22⋊C4—182no—
703C22⋊C4—182no—
704C22⋊C4—182no—
705C22⋊C4—182no—
706C22⋊C4—182no—
707C42—182no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C2×#23511yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C2×D3×D411yescharacteristic
727C22×C3#100411yescharacteristic
728C22×C3C2×D3×Q811yescharacteristic
729C22×C3C2×D3×Q811yescharacteristic
730C22×C3#100711yescharacteristic
731C22×C3D3×#4111yescharacteristic
732C22×C3D3×#4111yescharacteristic
733C22×C3D3×#4111yescharacteristic
734C22×C3#100911yescharacteristic
735C22×C3#101011yescharacteristic
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—34no—
740C2×D3—34no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—64no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—122no—
764C3×C4—34no—
765C3×C4—42no—
766C3×C4—41no—
767C3×C4—41no—
768C3×C4—41no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—81no—
776C3×C4—81no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—41no—
784Dic3—41no—
785Dic3—41no—
786Dic3—64no—
787Dic3—62no—
788Dic3—62no—
789Dic3—121no—
790Dic3—121no—
791Dic3—121no—
792Dic3—121no—
793Dic3—241no—
794Dic3—241no—
795Dic3#88414yes—
796C32#241711yescharacteristic, complemented, Sylow
797C23—32no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—92no—
805C23—92no—
806C23—92no—
807C23—181no—
808C23—181no—
809C23—181no—
810C23—181no—
811C23C22×D3211yescharacteristic
812Q8—364no—
813D4—188no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—92no—
845C2×C4—124no—
846C2×C4—188no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—181no—
852C2×C4—181no—
853C2×C4—181no—
854C2×C4—181no—
855C2×C4—364no—
856C2×C4—364no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—122no—
865C2×C3C2×#88411yescharacteristic
866C2×C3#551111yescharacteristic
867C2×C3#552911yescharacteristic
868C2×C3D3×#12111yescharacteristic
869C2×C3#560811yescharacteristic
870C2×C3#561211yescharacteristic
871C2×C3D3×C22⋊Q811yescharacteristic
872C2×C3D3×C22⋊Q811yescharacteristic
873C2×C3#562911yescharacteristic
874C2×C3#563211yescharacteristic
875C2×C3#565411yescharacteristic
876C2×C3#569011yescharacteristic
877C2×C3#569311yescharacteristic
878C2×C3#572711yescharacteristic
879D3—42no—
880D3—64no—
881D3—64no—
882D3—124no—
883C22—62no—
884C22—62no—
885C22—62no—
886C22—94no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—182no—
892C22—182no—
893C22—182no—
894C22—182no—
895C22—182no—
896C22—182no—
897C22#6429711yescharacteristic
898C22D3×#23511yescharacteristic
899C22#6430611yescharacteristic
900C22D32×D411yescharacteristic
901C22D32×D411yescharacteristic
902C22#6431411yescharacteristic
903C22D32×Q811yescharacteristic
904C4—34no—
905C4—41no—
906C4—41no—
907C4—41no—
908C4—62no—
909C4—62no—
910C4—62no—
911C4—121no—
912C4—121no—
913C4—121no—
914C4—182no—
915C4—361no—
916C4—361no—
917C3—21no—
918C3#7388811yescharacteristic, complemented
919C3#7774211yescharacteristic, complemented
920C2—122no—
921C2—184no—
922C2#1059387211yescharacteristic
923C2#1059406911yescharacteristic
924C2D3×#88411yescharacteristic
925C2#1059427911yescharacteristic
926C2#1059437811yescharacteristic
927C2#1059453811yescharacteristic
928C2#1059462411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC22×#626C22
hypercenter#95D32
hypocenterC32#2417
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63895C2semidirect
3. C2×#63883C2semidirect
4. C2×#63851C2semidirect
5. #10592366C2semidirect
6. C3×#4667C2semidirect
7. C3×#4657C2semidirect
9. #10591367C2semidirect
10. #10591340C2semidirect
11. #10591308C2semidirect
12. #10591306C2semidirect
14. #10591235C2semidirect
15. #10591234C2semidirect
81. #4667D3semidirect
85. #4657D3semidirect
114. C2×#626Q8semidirect
136. Dic3⋊Dic3D4semidirect
438. C2×C3⋊D3C22⋊Q8semidirect
796. C32#2417semidirect
918. C3#73888semidirect
919. C3#77742semidirect

Maximal subgroups

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

subgroupindex
C2×#639042
C2×#638952
C2×#638832
C2×#638512
#105923662
C3×#46672
C3×#46572
#105913872
#105913672
#105913402
#105913082
#105913062
#105912752
#105912352
#105912342
#777423
#738883