Finite Group Databasebeta

← #11813009

Subgroups — #11813009

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3C3×#4986C211yesmaximal, characteristic, complemented
4C3×#4978C211yesmaximal, characteristic, complemented
5#10591380C211yesmaximal, characteristic, complemented
6#10591380C211yesmaximal, characteristic, complemented
7#10591380C211yesmaximal, characteristic, complemented
8#10591380C211yesmaximal, characteristic, complemented
9#10591371C211yesmaximal, characteristic, complemented
10#10591370C211yesmaximal, characteristic, complemented
11#10591326C211yesmaximal, characteristic, complemented
12#10591321C211yesmaximal, characteristic, complemented
13#10591290C211yesmaximal, characteristic, complemented
14#10591208C211yesmaximal, characteristic, complemented
15#10591194C211yesmaximal, characteristic, complemented
16#78343—31nomaximal
17#75320—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28#64104—24no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×#3722C2211yescharacteristic
42#63894—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
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#895—31no—
56C2×#895—31no—
57C2×#895—61no—
58C2×#893—31no—
59C2×C4×D12—31no—
60C3×#400—31no—
61C3×#387—31no—
62#4992—31no—
63#4991—31no—
64#4989—31no—
65#4986D311yescharacteristic, complemented
66#4978D311yescharacteristic, complemented
67#4940—31no—
68#4675—31no—
69#4674—31no—
70#4674—31no—
71#4672—31no—
72#4670—31no—
73#4668—31no—
74#4665—31no—
75#4665—31no—
76#4665—31no—
77#4665—31no—
78#4665—31no—
79#4665—31no—
80#4665—31no—
81#4665—31no—
82#4664—31no—
83#4664—31no—
84D3×#95—31no—
85D3×#95—31no—
86C23×C3⋊D3C2311yescharacteristic
87C23×C3⋊D3C2311yescharacteristic
88C23×C3⋊D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)—22no—
100C2×C4⋊(C3⋊D3)—41no—
101C2×C4⋊(C3⋊D3)D414yes—
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3—22no—
104C2×C4×C3⋊D3—41no—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×#624—22no—
114C2×#624—22no—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—22no—
118C2×#624—41no—
119C2×#624—41no—
120C2×#624—41no—
121C2×#624—41no—
122C32×C4⋊C4—22no—
123#3752—22no—
124#3752—22no—
125C3×C4⋊Dic3—22no—
126C3×Dic3⋊C4—22no—
127C3×C4×Dic3—22no—
128Dic3⋊Dic3—41no—
129#3722—22no—
130#3722—22no—
131#3722—22no—
132#3722—22no—
133#3722—41no—
134#3722—41no—
135#3722—41no—
136#3722—41no—
137#3722—41no—
138#2444—91noSylow
139C22×D12—31no—
140C22×D12—31no—
141C22×D12—31no—
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—31no—
145C22×D12—61no—
146C22×D12—61no—
147C22×D12—61no—
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—31no—
155C22×C4×D3—31no—
156C22×C4×D3—61no—
157C2×C3×C4⋊C4—21no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4C2×D311yescharacteristic
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C42—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—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—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3C2×D311yescharacteristic
192#895—64no—
193#895—64no—
194#895—68no—
195#893—64no—
196C4×D12—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⋊#95C2×D311yescharacteristic
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⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D412yes—
240C22×C3⋊D3C2×D412yes—
241C22×C3⋊D3#4112yes—
242C22×C3⋊D3#4112yes—
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×C4C2×D412yes—
251C2×C32×C4#4112yes—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—28no—
256C4⋊(C3⋊D3)—44no—
257C4⋊(C3⋊D3)—44no—
258C4×C3⋊D3—44no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
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—21no—
282C2×C3×Dic3#4112yes—
283#624—44no—
284#624—44no—
285#624—44no—
286C2×#121—91no—
287C2×C4×D4—91no—
288#400—31no—
289#397—91no—
290#397—91no—
291#394—91no—
292#388—91no—
293#387—31no—
294#386—91no—
295#386—91no—
296#386—91no—
297#386—91no—
298#385—91no—
299#381—91no—
300C2×#95—91no—
301C23×D3—31no—
302C23×D3—31no—
303C23×D3—31no—
304C23×D3—31no—
305C23×D3—31no—
306C23×D3—31no—
307C23×D3—61no—
308C23×D3—61no—
309C23×D3—61no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
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×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C2×D12—34no—
339C2×D12—34no—
340C2×D12—64no—
341C2×D12—62no—
342C2×D12—62no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—62no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—62no—
350C2×D12—62no—
351C2×D12—62no—
352C2×D12—62no—
353C2×D12—64no—
354C2×D12—64no—
355C2×D12—62no—
356C2×D12—62no—
357C2×D12—122no—
358C2×D12—122no—
359C2×D12—122no—
360C2×D12—122no—
361C2×D12—122no—
362C2×D12—121no—
363C2×D12—121no—
364C2×D12—122no—
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—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—64no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—122no—
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—121no—
388C2×C4×D3—121no—
389C2×C4×D3—121no—
390C2×C4×D3—121no—
391C2×C4×D3—122no—
392C3×C4⋊C4—24no—
393C3×C4⋊C4—22no—
394C3×C4⋊C4—22no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C42—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
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—64no—
408(C2×D3)⋊C4—64no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
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—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422C4⋊Dic3—22no—
423C4⋊Dic3—121no—
424Dic3⋊C4—22no—
425Dic3⋊C4—121no—
426C4×Dic3—22no—
427C22×C32C22×D411yescharacteristic
428C22×C32C2×#4111yescharacteristic
429C22×C32C2×#4111yescharacteristic
430C22×C32C2×#4111yescharacteristic
431C22×C32C2×#4111yescharacteristic
432C22×C32H(5,𝔽2)11yescharacteristic
433C22×C32H(5,𝔽2)11yescharacteristic
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—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
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—
453C2×C3⋊D3—41no—
454C2×C3⋊D3#12314yes—
455C32×C4—22no—
456C32×C4—22no—
457C32×C4—41no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—41no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C22×D4—91no—
468C22×D4—91no—
469C22×D4—91no—
470C23×C4—91no—
471C23×C4—91no—
472C23×C4—91no—
473C23×C4—91no—
474#121—184no—
475C4×D4—184no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4D3211yescharacteristic
480C2×C22⋊C4—91no—
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×C22⋊C4—91no—
490C2×C22⋊C4—91no—
491C2×C42—31no—
492#95—31no—
493#95—31no—
494#95—31no—
495#95—31no—
496#95—31no—
497#95—31no—
498#95—31no—
499#95—31no—
500#95—31no—
501#95—91no—
502#95—91no—
503#95—91no—
504C23×C3—21no—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3—32no—
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—32no—
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—32no—
515C22×D3—62no—
516C22×D3—62no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
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—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—61no—
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—61no—
554C22×D3—121no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3—121no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
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—22no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—32no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
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×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4#23512yes—
618C2×C3×C4D3×D412yes—
619C2×C3×C4D3×D412yes—
620C2×C3×C4#23912yes—
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—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—62no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3#23912yes—
654D12—68no—
655D12—68no—
656D12—128no—
657D12—124no—
658D12—124no—
659D12—128no—
660D12—124no—
661D12—124no—
662D12—128no—
663C4×D3—124no—
664C4×D3—124no—
665C4×D3—124no—
666C4×D3—124no—
667C4×D3—124no—
668C4×D3—124no—
669C4×D3—124no—
670C4×D3—124no—
671C4×D3—128no—
672C2×C32C2×#12311yescharacteristic
673C2×C32#52911yescharacteristic
674C2×C32#53811yescharacteristic
675C2×C32#54611yescharacteristic
676C2×C32#54611yescharacteristic
677C2×C32#55311yescharacteristic
678C2×C32#55311yescharacteristic
679C3⋊D3—24no—
680C3⋊D3—42no—
681C3⋊D3—81no—
682C24—91no—
683C24—91no—
684C24—91no—
685C2×D4—94no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—361no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—91no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—182no—
706C22×C4—182no—
707C22×C4—182no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—361no—
711C22×C4—361no—
712C22×C4—361no—
713C22×C4—361no—
714C22×C4—361no—
715C22×C4C2×D3211yescharacteristic
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3211yescharacteristic
718C4⋊C4—22no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—361no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—361no—
729C22⋊C4—361no—
730C22⋊C4—361no—
731C22⋊C4—361no—
732C22⋊C4—361no—
733C42—62no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3C2×#23511yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C2×#23911yescharacteristic
745C22×C3C2×#23911yescharacteristic
746C22×C3D3×#4111yescharacteristic
747C22×C3D3×#4111yescharacteristic
748C22×C3D3×#4111yescharacteristic
749C22×C3D3×#4111yescharacteristic
750C22×C3D3×#4111yescharacteristic
751C22×C3#100911yescharacteristic
752C22×C3#100911yescharacteristic
753C22×C3#100911yescharacteristic
754C22×C3#100911yescharacteristic
755C2×D3—34no—
756C2×D3—34no—
757C2×D3—64no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
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—122no—
777C2×D3—122no—
778C2×D3—122no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—122no—
783C2×D3—122no—
784C2×D3—122no—
785C2×D3—121no—
786C2×D3—121no—
787C2×D3—121no—
788C2×D3—121no—
789C2×D3—121no—
790C2×D3—121no—
791C2×D3—121no—
792C2×D3—121no—
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—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—241no—
811C2×D3—241no—
812C2×D3—241no—
813C2×D3—241no—
814C2×D3—241no—
815C2×D3—241no—
816C2×D3—241no—
817C2×D3—241no—
818C3×C4—24no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—22no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—121no—
829C3×C4—121no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835Dic3—22no—
836Dic3—41no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—122no—
844Dic3—121no—
845Dic3—121no—
846C32#244411yescharacteristic, complemented, Sylow
847C23—92no—
848C23—92no—
849C23—92no—
850C23—92no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23—181no—
855C23—181no—
856C23—181no—
857C23—181no—
858C23—181no—
859C23—181no—
860C23—181no—
861C23—181no—
862C23—181no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23C22×D3211yescharacteristic
869D4—188no—
870D4—364no—
871D4—364no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—32no—
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—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—364no—
907C2×C4—364no—
908C2×C4—364no—
909C2×C4—364no—
910C2×C4#379912yes—
911C2×C4#381112yes—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3#553011yescharacteristic
920C2×C3#555011yescharacteristic
921C2×C3#558011yescharacteristic
922C2×C3#563011yescharacteristic
923C2×C3#563011yescharacteristic
924C2×C3D3×#12311yescharacteristic
925C2×C3D3×#12311yescharacteristic
926C2×C3#567611yescharacteristic
927C2×C3#569111yescharacteristic
928C2×C3#569511yescharacteristic
929C2×C3#569511yescharacteristic
930C2×C3#570411yescharacteristic
931C2×C3#570411yescharacteristic
932C2×C3#570911yescharacteristic
933D3—64no—
934D3—64no—
935D3—124no—
936D3—122no—
937D3—122no—
938D3—242no—
939D3—242no—
940D3—241no—
941D3—241no—
942C22—94no—
943C22—182no—
944C22—182no—
945C22—182no—
946C22—182no—
947C22—182no—
948C22—182no—
949C22—182no—
950C22—182no—
951C22—182no—
952C22—361no—
953C22—361no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22—361no—
960C22—361no—
961C22—361no—
962C22—361no—
963C22C2×#379911yescharacteristic
964C22#6430811yescharacteristic
965C22#6431211yescharacteristic
966C22#6431211yescharacteristic
967C22D3×#23911yescharacteristic
968C22#6432011yescharacteristic
969C22C2×#381111yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—62no—
974C4—121no—
975C4—121no—
976C4—121no—
977C4—121no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—361no—
982C3—21no—
983C3#7532011yescharacteristic, complemented
984C3#7834311yescharacteristic, complemented
985C2—184no—
986C2—362no—
987C2—721no—
988C2#1059446411yescharacteristic
989C2#1059446811yescharacteristic
990C2#1059457811yescharacteristic
991C2#1059465811yescharacteristic
992C2#1059501811yescharacteristic
993C2#1059516911yescharacteristic
994C2#1059543111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#64104C2
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
2. C2×#63894C2semidirect
3. C3×#4986C2semidirect
4. C3×#4978C2semidirect
5. #10591380C2semidirect
6. #10591380C2semidirect
7. #10591380C2semidirect
8. #10591380C2semidirect
9. #10591371C2semidirect
10. #10591370C2semidirect
11. #10591326C2semidirect
12. #10591321C2semidirect
13. #10591290C2semidirect
14. #10591208C2semidirect
15. #10591194C2semidirect
65. #4986D3semidirect
66. #4978D3semidirect
846. C32#2444semidirect
983. C3#75320semidirect
984. C3#78343semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#638942
C3×#49862
C3×#49782
#105913802
#105913712
#105913702
#105913262
#105913212
#105912902
#105912082
#105911942
#783433
#753203