Finite Group Databasebeta

← #11812994

Subgroups — #11812994

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic, complemented
2C2×#63910C211yesmaximal, characteristic
3C3×#4992C211yesmaximal, characteristic, complemented
4C3×#4985C211yesmaximal, characteristic, complemented
5#10591387C211yesmaximal, characteristic, complemented
6#10591387C211yesmaximal, characteristic, complemented
7#10591380C211yesmaximal, characteristic, complemented
8#10591375C211yesmaximal, characteristic, complemented
9#10591370C211yesmaximal, characteristic, complemented
10#10591334C211yesmaximal, characteristic, complemented
11#10591312C211yesmaximal, characteristic, complemented
12#10591287C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591219C211yesmaximal, characteristic, complemented
15#10591208C211yesmaximal, characteristic, complemented
16#78343—31nomaximal
17#77675—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64102—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42#63910—24no—
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#895—31no—
56C2×#893—31no—
57C2×#893—31no—
58C2×#893—61no—
59C2×#884—31no—
60C3×#400—31no—
61C3×#397—31no—
62#4992D311yescharacteristic, complemented
63#4985D311yescharacteristic, complemented
64#4978—31no—
65#4961—31no—
66#4956—31no—
67#4956—31no—
68#4956—31no—
69#4944—31no—
70#4675—31no—
71#4674—31no—
72#4672—31no—
73#4670—31no—
74#4668—31no—
75#4668—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4664—31no—
82#4664—31no—
83D3×#95—31no—
84D3×#95—31no—
85#4653—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)D414yes—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—22no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—41no—
102C2×C4×C3⋊D3—41no—
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626—22no—
115C2×#626—41no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—41no—
120C2×#624—41no—
121C2×#624—41no—
122C32×C4⋊C4—22no—
123#3752—22no—
124#3752—22no—
125C4×C3⋊Dic3—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×Dic3⋊C4—22no—
130Dic3⋊Dic3—22no—
131Dic3⋊Dic3—41no—
132#3722—22no—
133#3722—22no—
134#3722—41no—
135#3722—41no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—41no—
138#2444—91noSylow
139C22×#67—31no—
140C22×#67—31no—
141C22×D12—31no—
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12—61no—
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—31no—
153C22×C4×D3—31no—
154C22×C4×D3—61no—
155C22×C4×D3—61no—
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4C2×D311yescharacteristic
159C2×C3×C4⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
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—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×(C2×D3)⋊C4C2×D311yescharacteristic
182C2×(C2×D3)⋊C4C2×D311yescharacteristic
183C2×(C2×D3)⋊C4C2×D311yescharacteristic
184C2×C4⋊Dic3—31no—
185C2×C4⋊Dic3—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4C2×D311yescharacteristic
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—61no—
192#895—64no—
193#893—64no—
194#893—64no—
195#893—68no—
196#884—64no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
222C22×C3⋊D3—21no—
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3C2×D412yes—
233C22×C3⋊D3C2×D412yes—
234C22×C3⋊D3#4112yes—
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×D3—21no—
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×C4C2×D412yes—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3#4112yes—
258C4⋊(C3⋊D3)—28no—
259C4×C3⋊D3—44no—
260C4×C3⋊D3—44no—
261C2×C3×Dic3—21no—
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×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3#4112yes—
282#626—44no—
283#626—44no—
284#624—44no—
285#624—44no—
286C2×#121—91no—
287C2×C4×D4—91no—
288#400—31no—
289#397—31no—
290#397—91no—
291#394—91no—
292#388—91no—
293#387—91no—
294#386—91no—
295#386—91no—
296#386—91no—
297#386—91no—
298#385—91no—
299#381—91no—
300C2×#95—91no—
301C24×C3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—31no—
305C23×D3—31no—
306C23×D3—61no—
307C23×D3—61no—
308C23×D3C22×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
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—31no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—62no—
326C2×#67—62no—
327C2×#67—62no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—121no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—31no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C22×Dic3C22×D311yescharacteristic
340C22×Dic3C22×D311yescharacteristic
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C2×D12—34no—
345C2×D12—34no—
346C2×D12—64no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—62no—
350C2×D12—62no—
351C2×D12—64no—
352C2×D12—64no—
353C2×D12—62no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—121no—
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—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—64no—
373C2×C4×D3—64no—
374C2×C4×D3—62no—
375C2×C4×D3—122no—
376C2×C4×D3—122no—
377C2×C4×D3—121no—
378C2×C4×D3—121no—
379C2×C4×D3—121no—
380C2×C4×D3—121no—
381C2×C4×D3—121no—
382C2×C4×D3—121no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—122no—
388C2×C4×D3—122no—
389C3×C4⋊C4—24no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—121no—
395C3×C22⋊C4—121no—
396#217—62no—
397#217—121no—
398(C2×D3)⋊C4—22no—
399(C2×D3)⋊C4—41no—
400(C2×D3)⋊C4—41no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—64no—
411(C2×D3)⋊C4—64no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417C4⋊Dic3—62no—
418C4⋊Dic3—121no—
419Dic3⋊C4—22no—
420Dic3⋊C4—62no—
421Dic3⋊C4—121no—
422C4×Dic3—64no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C22×C32C22×D411yescharacteristic
426C22×C32C2×#4111yescharacteristic
427C22×C32C2×#4111yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32H(5,𝔽2)11yescharacteristic
431C22×C32H(5,𝔽2)11yescharacteristic
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⋊D3—22no—
439C2×C3⋊D3—22no—
440C2×C3⋊D3—22no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3#12314yes—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C32×C4—22no—
454C32×C4—41no—
455C32×C4—41no—
456C3⋊Dic3—22no—
457C3⋊Dic3—41no—
458C3×Dic3—22no—
459C3×Dic3—41no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C22×D4—91no—
466C22×D4—91no—
467C22×D4—91no—
468C23×C4—91no—
469C23×C4—91no—
470C23×C4—91no—
471C23×C4—91no—
472#121—184no—
473C4×D4—184no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4D3211yescharacteristic
478C2×C22⋊C4—31no—
479C2×C22⋊C4—31no—
480C2×C22⋊C4—31no—
481C2×C22⋊C4—91no—
482C2×C22⋊C4—91no—
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—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—31no—
498#95—91no—
499#95—91no—
500#95—91no—
501#95—91no—
502C23×C3—21no—
503C23×C3—61no—
504C23×C3—61no—
505C23×C3—61no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—61no—
509C23×C3—61no—
510C23×C3C23×D311yescharacteristic
511C23×C3C23×D311yescharacteristic
512C22×D3—21no—
513C22×D3—21no—
514C22×D3—21no—
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—32no—
520C22×D3—32no—
521C22×D3—32no—
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—32no—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—62no—
531C22×D3—61no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—22no—
582C2×C3×C4—32no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4D3×D412yes—
608C2×C3×C4D3×D412yes—
609#67—124no—
610#67—124no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—62no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3#23912yes—
650D12—68no—
651D12—68no—
652D12—616no—
653D12—124no—
654D12—124no—
655C4×D3—124no—
656C4×D3—124no—
657C4×D3—124no—
658C4×D3—124no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—124no—
663C4×D3—128no—
664C4×D3—128no—
665C2×C32C2×#12311yescharacteristic
666C2×C32#52911yescharacteristic
667C2×C32#53811yescharacteristic
668C2×C32#54611yescharacteristic
669C2×C32#54611yescharacteristic
670C2×C32#55311yescharacteristic
671C2×C32#55311yescharacteristic
672C3⋊D3—24no—
673C3⋊D3—42no—
674C3×D3—81no—
675C24—31no—
676C24—91no—
677C24—91no—
678C2×D4—94no—
679C2×D4—182no—
680C2×D4—182no—
681C2×D4—182no—
682C2×D4—182no—
683C2×D4—182no—
684C2×D4—182no—
685C2×D4—182no—
686C2×D4—361no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—182no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—361no—
704C22×C4—361no—
705C22×C4—361no—
706C22×C4—361no—
707C22×C4—361no—
708C22×C4C2×D3211yescharacteristic
709C22×C4C2×D3211yescharacteristic
710C22×C4C2×D3211yescharacteristic
711C4⋊C4—22no—
712C4⋊C4—62no—
713C4⋊C4—182no—
714C4⋊C4—361no—
715C22⋊C4—62no—
716C22⋊C4—121no—
717C22⋊C4—121no—
718C22⋊C4—182no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—361no—
724C22⋊C4—361no—
725C22⋊C4—361no—
726C42—182no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C22×C3#100411yescharacteristic
744C22×C3C2×#23911yescharacteristic
745C22×C3D3×#4111yescharacteristic
746C22×C3D3×#4111yescharacteristic
747C22×C3D3×#4111yescharacteristic
748C22×C3D3×#4111yescharacteristic
749C22×C3D3×#4111yescharacteristic
750C22×C3D3×#4111yescharacteristic
751C22×C3D3×#4111yescharacteristic
752C22×C3#100911yescharacteristic
753C22×C3#100911yescharacteristic
754C22×C3#100911yescharacteristic
755C2×D3—34no—
756C2×D3—34no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—64no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—64no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—62no—
781C2×D3—62no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—122no—
785C2×D3—122no—
786C2×D3—122no—
787C2×D3—122no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—122no—
793C2×D3—122no—
794C2×D3—122no—
795C2×D3—122no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—121no—
800C2×D3—121no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C3×C4—24no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—42no—
808C3×C4—42no—
809C3×C4—41no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—62no—
814C3×C4—121no—
815C3×C4—121no—
816C3×C4—121no—
817C3×C4—121no—
818C3×C4—121no—
819C3×C4—121no—
820Dic3—22no—
821Dic3—41no—
822Dic3—41no—
823Dic3—41no—
824Dic3—41no—
825Dic3—41no—
826Dic3—41no—
827Dic3—64no—
828Dic3—62no—
829Dic3—62no—
830Dic3—122no—
831Dic3—121no—
832Dic3—121no—
833C32#244411yescharacteristic, complemented, Sylow
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—92no—
842C23—92no—
843C23—92no—
844C23—92no—
845C23—181no—
846C23—181no—
847C23—181no—
848C23—181no—
849C23—181no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23—181no—
855C23C22×D3211yescharacteristic
856D4—188no—
857D4—364no—
858D4—364no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—32no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—92no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—364no—
895C2×C4—364no—
896C2×C4—364no—
897C2×C4—364no—
898C2×C4#381112yes—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—241no—
907C2×C3#561211yescharacteristic
908C2×C3#563011yescharacteristic
909C2×C3D3×#12311yescharacteristic
910C2×C3D3×#12311yescharacteristic
911C2×C3#565711yescharacteristic
912C2×C3#566111yescharacteristic
913C2×C3#567611yescharacteristic
914C2×C3#567611yescharacteristic
915C2×C3#569111yescharacteristic
916C2×C3#569511yescharacteristic
917C2×C3#570411yescharacteristic
918C2×C3#570611yescharacteristic
919C2×C3#570911yescharacteristic
920C2×C3#570911yescharacteristic
921D3—64no—
922D3—64no—
923D3—81no—
924D3—124no—
925D3—124no—
926D3—122no—
927D3—122no—
928C22—94no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—182no—
937C22—182no—
938C22—182no—
939C22—182no—
940C22—182no—
941C22—182no—
942C22—182no—
943C22—182no—
944C22—182no—
945C22—361no—
946C22—361no—
947C22—361no—
948C22—361no—
949C22#6430611yescharacteristic
950C22#6430611yescharacteristic
951C22#6431211yescharacteristic
952C22#6431411yescharacteristic
953C22D3×#23911yescharacteristic
954C22#6432011yescharacteristic
955C22C2×#381111yescharacteristic
956C4—22no—
957C4—41no—
958C4—41no—
959C4—62no—
960C4—121no—
961C4—121no—
962C4—121no—
963C4—121no—
964C4—121no—
965C4—121no—
966C4—182no—
967C4—361no—
968C3—21no—
969C3#7767511yescharacteristic, complemented
970C3#7834311yescharacteristic, complemented
971C2—184no—
972C2—241no—
973C2—362no—
974C2#1059446111yescharacteristic
975C2#1059446511yescharacteristic
976C2#1059447511yescharacteristic
977C2#1059465711yescharacteristic
978C2#1059507911yescharacteristic
979C2#1059524311yescharacteristic
980C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63910C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
3. C3×#4992C2semidirect
4. C3×#4985C2semidirect
5. #10591387C2semidirect
6. #10591387C2semidirect
7. #10591380C2semidirect
8. #10591375C2semidirect
9. #10591370C2semidirect
10. #10591334C2semidirect
11. #10591312C2semidirect
12. #10591287C2semidirect
13. #10591275C2semidirect
14. #10591219C2semidirect
15. #10591208C2semidirect
62. #4992D3semidirect
63. #4985D3semidirect
833. C32#2444semidirect
969. C3#77675semidirect
970. C3#78343semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639102
C3×#49922
C3×#49852
#105913872
#105913802
#105913752
#105913702
#105913342
#105913122
#105912872
#105912752
#105912192
#105912082
#783433
#776753