Finite Group Databasebeta

← #11803386

Subgroups — #11803386

Order 1152.

1473 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×#63853C211yesmaximal, characteristic
4C3×#4989C211yesmaximal, characteristic, complemented
5C3×#4978C211yesmaximal, characteristic, complemented
6#10591387C211yesmaximal, characteristic
7#10591332C211yesmaximal, characteristic, complemented
8#10591316C211yesmaximal, characteristic, complemented
9#10591290C211yesmaximal, characteristic, complemented
10#10591281C211yesmaximal, characteristic, complemented
11#10591278C211yesmaximal, characteristic, complemented
12#10591268C211yesmaximal, characteristic, complemented
13#10591260C211yesmaximal, characteristic, complemented
14#10591234C211yesmaximal, characteristic, complemented
15#10591219C211yesmaximal, characteristic, complemented
16#75297—31nomaximal
17#74593—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C4⋊C4×C3⋊D3—24no—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C4×#626—24no—
45#63853C418yescomplemented
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C4×#67—31no—
57C2×#894—31no—
58C2×D3×C4⋊C4—31no—
59C2×D3×C4⋊C4—31no—
60C2×D3×C4⋊C4—61no—
61C2×#883—31no—
62C2×C4×D12—31no—
63C3×#387—31no—
64C3×#385—31no—
65#5210—31no—
66#4989—31no—
67#4989D311yescharacteristic, complemented
68#4984—31no—
69#4978D311yescharacteristic, complemented
70#4972—31no—
71#4956—31no—
72#4951—31no—
73#4944—31no—
74#4933—31no—
75#4670—31no—
76#4669—31no—
77#4668—31no—
78#4668—31no—
79#4666—31no—
80#4666—31no—
81#4665—31no—
82#4664—31no—
83#4664—31no—
84#4653—31no—
85#4647—31no—
86#4647—31no—
87C23×C3⋊D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C2×C4×C3⋊D3—22no—
96C2×C4×C3⋊D3—22no—
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—41no—
99C2×C4×C3⋊D3—41no—
100C2×C4×C3⋊D3—41no—
101C2×C4×C3⋊D3—41no—
102C2×C4×C3⋊D3C2×C414yescomplemented
103C2×C4×C3⋊D3D414yes—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—41no—
113C2×C3×C4×D3—41no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626C2×C414yes—
117C32×C4⋊C4—22no—
118C4⋊(C3⋊Dic3)—22no—
119#3750—22no—
120#3750—22no—
121C3×(C2×D3)⋊C4—41no—
122C3×(C2×D3)⋊C4C2×C414yescomplemented
123C3×Dic3⋊C4—41no—
124C3×Dic3⋊C4C2×C414yescomplemented
125C3×C4×Dic3—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—41no—
128Dic3⋊Dic3C2×C414yescomplemented
129#3722—22no—
130#3722—22no—
131#3722C2×C414yescomplemented
132(C2×D3)⋊Dic3—22no—
133(C2×D3)⋊Dic3—41no—
134(C2×D3)⋊Dic3C2×C414yescomplemented
135Dic32—41no—
136Dic32—41no—
137#2322—91noSylow
138C23×C3×C4—31no—
139C22×#67—31no—
140C22×D12—31no—
141C22×C4×D3—31no—
142C22×C4×D3—31no—
143C22×C4×D3—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—61no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C22×C4×D3C2×D311yescharacteristic
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4C2×D311yescharacteristic
155C2×C3×C4⋊C4C2×D311yescharacteristic
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C42—31no—
159C2×#217—31no—
160C2×#217—31no—
161C2×#217—31no—
162C4×#67—64no—
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)⋊C4C2×D311yescharacteristic
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4—61no—
189C2×Dic3⋊C4C2×D311yescharacteristic
190C2×Dic3⋊C4C2×D311yescharacteristic
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—31no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3C2×D311yescharacteristic
196#894—38no—
197D3×C4⋊C4—64no—
198D3×C4⋊C4—64no—
199D3×C4⋊C4—68no—
200#883—38no—
201C4×D12—64no—
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⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95C2×D311yescharacteristic
217C3⋊#95C2×D311yescharacteristic
218C3⋊#95C2×D311yescharacteristic
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C3⋊#95C2×D311yescharacteristic
222C23×C32C2411yescharacteristic
223C22×C3⋊D3—21no—
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3C22×C412yes—
228C22×C3⋊D3C2×D412yes—
229C22×C3⋊D3#4112yes—
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×D3C22×C412yes—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C22×C412yes—
245C2×C32×C4C2×D412yes—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C22×C412yes—
254C2×C3⋊Dic3C2×D412yes—
255C4×C3⋊D3—28no—
256C4×C3⋊D3—44no—
257C4×C3⋊D3—44no—
258C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C3×C4×D3—44no—
280#626—28no—
281C2×#123—91no—
282C2×C4×D4—91no—
283C22×C4⋊C4—91no—
284#389—91no—
285#389—91no—
286#388—91no—
287#388—91no—
288#387—31no—
289#387—91no—
290#386—91no—
291#385—31no—
292#385—91no—
293#385—91no—
294#381—91no—
295C4×C22⋊C4—91no—
296C24×C3—31no—
297C23×D3—31no—
298C23×D3—31no—
299C23×D3—61no—
300C23×D3C22×D311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—62no—
312C22×C3×C4—121no—
313C22×C3×C4—121no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C2×#67—34no—
321C2×#67—62no—
322C2×#67—62no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C2×D12—34no—
340C2×D12—62no—
341C2×D12—62no—
342C2×C4×D3—22no—
343C2×C4×D3—34no—
344C2×C4×D3—34no—
345C2×C4×D3—34no—
346C2×C4×D3—34no—
347C2×C4×D3—41no—
348C2×C4×D3—41no—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3—62no—
352C2×C4×D3—62no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—64no—
356C2×C4×D3—64no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—64no—
360C2×C4×D3—121no—
361C2×C4×D3—121no—
362C2×C4×D3—121no—
363C2×C4×D3—121no—
364C2×C4×D3—121no—
365C2×C4×D3—121no—
366C2×C4×D3—121no—
367C2×C4×D3—121no—
368C2×C4×D3—122no—
369C2×C4×D3—122no—
370C2×C4×D3—122no—
371C2×C4×D3—122no—
372C3×C4⋊C4—24no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—121no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—121no—
379C3×C42—62no—
380#217—34no—
381#217—62no—
382#217—121no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—41no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391(C2×D3)⋊C4—62no—
392(C2×D3)⋊C4—121no—
393(C2×D3)⋊C4C4×D314yescomplemented
394C4⋊Dic3—34no—
395C4⋊Dic3—62no—
396C4⋊Dic3—62no—
397C4⋊Dic3—62no—
398C4⋊Dic3—64no—
399C4⋊Dic3—121no—
400Dic3⋊C4—34no—
401Dic3⋊C4—41no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—64no—
406Dic3⋊C4—64no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—121no—
410Dic3⋊C4C4×D314yescomplemented
411C4×Dic3—22no—
412C4×Dic3—121no—
413C4×Dic3—121no—
414C4×Dic3—121no—
415C4×Dic3—121no—
416C22×C32C23×C411yescharacteristic
417C22×C32C22×D411yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32H(5,𝔽2)11yescharacteristic
420C22×C32H(5,𝔽2)11yescharacteristic
421C22×C322−1+411yescharacteristic
422C22×C322−1+411yescharacteristic
423C2×C3⋊D3—22no—
424C2×C3⋊D3—22no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—22no—
427C2×C3⋊D3—22no—
428C2×C3⋊D3—22no—
429C2×C3⋊D3C4×D414yes—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C32×C4—22no—
438C32×C4—22no—
439C32×C4—41no—
440C3⋊Dic3—22no—
441C3⋊Dic3—22no—
442C3⋊Dic3—41no—
443C3×Dic3—22no—
444C3×Dic3—22no—
445C3×Dic3—22no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—91no—
451C23×C4—31no—
452C23×C4—91no—
453C23×C4—91no—
454C23×C4—91no—
455#123—98no—
456C4×D4—184no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—31no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—184no—
466C2×C4⋊C4D3211yescharacteristic
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—91no—
470C2×C22⋊C4—91no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473C2×C22⋊C4—91no—
474C2×C22⋊C4—91no—
475C2×C42—31no—
476C2×C42—91no—
477C2×C42—91no—
478#95—31no—
479#95—31no—
480#95—31no—
481#95—31no—
482#95—31no—
483#95—31no—
484#95—91no—
485#95—91no—
486#95—91no—
487#95—91no—
488C23×C3—21no—
489C23×C3—32no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3C23×D311yescharacteristic
497C23×C3C23×D311yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—32no—
505C22×D3—32no—
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—62no—
511C22×D3—62no—
512C22×D3—62no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—62no—
517C22×D3—61no—
518C22×D3—61no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—61no—
525C22×D3C2×C4×D312yes—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
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—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—22no—
544C2×C3×C4—22no—
545C2×C3×C4—32no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
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—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—124no—
571C2×C3×C4C2×C4×D312yes—
572C2×C3×C4C2×C4×D312yes—
573C2×C3×C4D3×D412yes—
574C2×C3×C4D3×D412yes—
575#67—68no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
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—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—62no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3C2×C4×D312yes—
622C2×Dic3C2×C4×D312yes—
623C2×Dic3C2×C4×D312yes—
624D12—68no—
625C4×D3—44no—
626C4×D3—68no—
627C4×D3—68no—
628C4×D3—616no—
629C4×D3—124no—
630C4×D3—124no—
631C4×D3—128no—
632C4×D3—128no—
633C4×D3—124no—
634C4×D3—124no—
635C2×C32C2×C4×D411yescharacteristic
636C2×C32#52011yescharacteristic
637C2×C32#52011yescharacteristic
638C2×C32#53411yescharacteristic
639C2×C32#53611yescharacteristic
640C2×C32#53911yescharacteristic
641C2×C32#53911yescharacteristic
642C3⋊D3—24no—
643C3×D3—42no—
644C24—31no—
645C24—91no—
646C2×D4—94no—
647C2×D4—182no—
648C2×D4—182no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—31no—
656C22×C4—62no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—94no—
660C22×C4—94no—
661C22×C4—91no—
662C22×C4—121no—
663C22×C4—121no—
664C22×C4—182no—
665C22×C4—182no—
666C22×C4—182no—
667C22×C4—361no—
668C22×C4—361no—
669C22×C4—361no—
670C22×C4—361no—
671C22×C4C2×D3211yescharacteristic
672C22×C4C2×D3211yescharacteristic
673C22×C4C2×D3211yescharacteristic
674C4⋊C4—22no—
675C4⋊C4—34no—
676C4⋊C4—94no—
677C4⋊C4—121no—
678C4⋊C4—182no—
679C4⋊C4—182no—
680C4⋊C4—182no—
681C4⋊C4—182no—
682C4⋊C4—361no—
683C22⋊C4—34no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—121no—
687C22⋊C4—182no—
688C22⋊C4—182no—
689C22⋊C4—182no—
690C22⋊C4—361no—
691C42—62no—
692C42—361no—
693C42—361no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3C22×C4×D311yescharacteristic
709C22×C3C22×C4×D311yescharacteristic
710C22×C3C2×D3×D411yescharacteristic
711C22×C3C2×D3×D411yescharacteristic
712C22×C3#100411yescharacteristic
713C22×C3#100411yescharacteristic
714C22×C3#100711yescharacteristic
715C22×C3#100711yescharacteristic
716C22×C3D3×#4111yescharacteristic
717C22×C3D3×#4111yescharacteristic
718C22×C3#100911yescharacteristic
719C22×C3#100911yescharacteristic
720C22×C3#101011yescharacteristic
721C22×C3#101011yescharacteristic
722C2×D3—22no—
723C2×D3—22no—
724C2×D3—22no—
725C2×D3—34no—
726C2×D3—34no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—64no—
732C2×D3—64no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—64no—
736C2×D3—64no—
737C2×D3—64no—
738C2×D3—62no—
739C2×D3—62no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C3×C4—24no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—42no—
756C3×C4—42no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4—121no—
765C3×C4—121no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—41no—
773Dic3—64no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3—121no—
781Dic3—121no—
782C32#232211yescharacteristic, complemented, Sylow
783C23—32no—
784C23—61no—
785C23—61no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—92no—
791C23—92no—
792C23—92no—
793C23—181no—
794C23—181no—
795C23—181no—
796C23—181no—
797C23C22×D3211yescharacteristic
798D4—188no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—124no—
830C2×C4—188no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—181no—
834C2×C4—181no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—364no—
839C2×C4—364no—
840C2×C4C4×D3212yes—
841C2×C4#381112yes—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—122no—
850C2×C3#550411yescharacteristic
851C2×C3#552311yescharacteristic
852C2×C3C4×D3×D411yescharacteristic
853C2×C3C4×D3×D411yescharacteristic
854C2×C3#554611yescharacteristic
855C2×C3#557411yescharacteristic
856C2×C3#558911yescharacteristic
857C2×C3#562811yescharacteristic
858C2×C3#562811yescharacteristic
859C2×C3#563811yescharacteristic
860C2×C3#565311yescharacteristic
861C2×C3#566011yescharacteristic
862C2×C3#569211yescharacteristic
863C2×C3#570711yescharacteristic
864D3—42no—
865D3—68no—
866D3—64no—
867D3—64no—
868C22—62no—
869C22—62no—
870C22—62no—
871C22—94no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—182no—
877C22—182no—
878C22—182no—
879C22—182no—
880C22—182no—
881C22—182no—
882C22C2×C4×D3211yescharacteristic
883C22#6430611yescharacteristic
884C22#6431411yescharacteristic
885C22#6431411yescharacteristic
886C22#6431511yescharacteristic
887C22#6431511yescharacteristic
888C22C2×#381111yescharacteristic
889C4—22no—
890C4—22no—
891C4—41no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—121no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—182no—
900C4—182no—
901C4—361no—
902C3—21no—
903C3#7459311yescharacteristic, complemented
904C3#7529711yescharacteristic, complemented
905C2—122no—
906C2—184no—
907C2#1059436111yescharacteristic
908C2#1059451011yescharacteristic
909C2#1059457211yescharacteristic
910C2#1059457311yescharacteristic
911C2C4×#381111yescharacteristic
912C2#1059524211yescharacteristic
913C2#1059540511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×C3⋊D3C2semidirect
4. C3×#4989C2semidirect
5. C3×#4978C2semidirect
7. #10591332C2semidirect
8. #10591316C2semidirect
9. #10591290C2semidirect
10. #10591281C2semidirect
11. #10591278C2semidirect
12. #10591268C2semidirect
13. #10591260C2semidirect
14. #10591234C2semidirect
15. #10591219C2semidirect
45. #63853C4semidirect
67. #4989D3semidirect
69. #4978D3semidirect
102. C2×C4×C3⋊D3C2×C4semidirect
122. C3×(C2×D3)⋊C4C2×C4semidirect
124. C3×Dic3⋊C4C2×C4semidirect
128. Dic3⋊Dic3C2×C4semidirect
131. #3722C2×C4semidirect
134. (C2×D3)⋊Dic3C2×C4semidirect
393. (C2×D3)⋊C4C4×D3semidirect
410. Dic3⋊C4C4×D3semidirect
782. C32#2322semidirect
903. C3#74593semidirect
904. C3#75297semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C4×#6262
C2×#638532
C3×#49892
C3×#49782
#105913872
#105913322
#105913162
#105912902
#105912812
#105912782
#105912682
#105912602
#105912342
#105912192
#752973
#745933