Finite Group Databasebeta

← #13178359

Subgroups — #13178359

Order 1728.

1448 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89041C212yesmaximal, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#64097C211yesmaximal, characteristic, complemented
5#11723696C211yesmaximal, characteristic, complemented
6#11723694C212yesmaximal, complemented
7C4×#6295C211yesmaximal, characteristic, complemented
8#11723691C211yesmaximal, characteristic, complemented
9#11723689C211yesmaximal, characteristic, complemented
10#11723688C212yesmaximal, complemented
11#11723686C212yesmaximal, complemented
12#10594517—31nomaximal
13#10594373—31nomaximal
14#10594370—31nomaximal
15C2×C3×C4⋊(C3⋊D3)C2212yes—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2212yes—
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2212yes—
21C2×#6295C2212yes—
22C2×#6295C2211yescharacteristic
23C2×#6294C2212yes—
24C2×#6294C2212yes—
25#89041—28no—
26C33×C4⋊C4C2211yescharacteristic
27C3×#3752C2212yes—
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2212yes—
31C3×#3750C2212yes—
32C3×C4×C3⋊Dic3C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2212yes—
35#88814C2211yescharacteristic
36#88814C2212yes—
37#88814C2212yes—
38#88814C2211yescharacteristic
39C2×#3799—32no—
40C2×#3796—32no—
41C2×#3795—32no—
42#64104D311yescharacteristic, complemented
43C4⋊C4×C3⋊D3D311yescharacteristic, complemented
44#64097D311yescharacteristic, complemented
45C3×#895—31no—
46C3×#895—31no—
47C3×#895—61no—
48C3×D3×C4⋊C4—31no—
49C3×D3×C4⋊C4—31no—
50C3×D3×C4⋊C4—61no—
51C3×#888—31no—
52C3×#888—31no—
53C3×#888—61no—
54#63916—31no—
55#63909—31no—
56#63908—31no—
57#63905—32no—
58C4×#626—31no—
59C4×#626—31no—
60C4×#625—31no—
61#63900—31no—
62#63898—31no—
63#63897—32no—
64#63896—32no—
65#63894—31no—
66Dic3×D12—31no—
67D3×C4⋊Dic3—31no—
68D3×C4⋊Dic3—31no—
69#63888—32no—
70#63887—32no—
71#63884—32no—
72#63884—32no—
73#63853—32no—
74#63850—32no—
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C2×C33×C4C2312yes—
79C2×C33×C4C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C3×C4⋊(C3⋊D3)—24no—
87C3×C4⋊(C3⋊D3)—22no—
88C3×C4×C3⋊D3—24no—
89C3×C4×C3⋊D3—22no—
90C3×C4×C3⋊D3—22no—
91C3×#634—24no—
92#6295—24no—
93#6295D414yescomplemented
94#6294—24no—
95#6294—24no—
96#5726—91no—
97#5611—91no—
98#5507—91no—
99C2×C4⋊(C3⋊D3)C2×D312yes—
100C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
101C2×C4×C3⋊D3C2×D312yes—
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×C4×C3⋊D3C2×D311yescharacteristic
104C2×#634C2×D312yes—
105C2×C3×D12—32no—
106C2×C3×D12—32no—
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—61no—
110C2×C3×D12—62no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3—62no—
119C2×C3×C4×D3—61no—
120C2×C3×Dic6—32no—
121C2×C3×Dic6—32no—
122C2×C3×Dic6—62no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—32no—
126C2×#626—32no—
127C2×#625—31no—
128C2×#625—32no—
129C2×#624—32no—
130C2×#624—32no—
131C2×D3×Dic3—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134C2×D3×Dic3—32no—
135#3799—68no—
136#3796—68no—
137#3795—68no—
138C32×C4⋊C4—21no—
139C32×C4⋊C4—21no—
140C32×C4⋊C4—21no—
141C32×C4⋊C4—41no—
142C32×C4⋊C4C2×D311yescharacteristic
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C2×D311yescharacteristic
145#3752C2×D312yes—
146C4⋊(C3⋊Dic3)C2×D311yescharacteristic
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic
148#3750C2×D312yes—
149#3750C2×D312yes—
150C4×C3⋊Dic3C2×D311yescharacteristic
151C3×(C2×D3)⋊C4—32no—
152C3×(C2×D3)⋊C4—32no—
153C3×(C2×D3)⋊C4—62no—
154C3×C4⋊Dic3—31no—
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×C4⋊Dic3—61no—
160C3×Dic3⋊C4—32no—
161C3×Dic3⋊C4—32no—
162C3×Dic3⋊C4—32no—
163C3×Dic3⋊C4—32no—
164C3×Dic3⋊C4—62no—
165C3×Dic3⋊C4—62no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—61no—
169#3724—32no—
170#3724—31no—
171Dic3⋊Dic3—32no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—32no—
175#3722—32no—
176#3722—31no—
177#3722—32no—
178#3722—31no—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—31no—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—21no—
190C2×C3×C3⋊D3—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3C2×D412yes—
196C2×C3×C3⋊D3C2×D412yes—
197C33×C4—22no—
198C33×C4#4112yescomplemented
199C3×C3⋊Dic3—22no—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3C2×D412yes—
205C2×#239—92no—
206C2×#237—92no—
207C2×#235—92no—
208C3×C4⋊Q8—91no—
209C3×#121—91no—
210C2×C3×C4⋊C4—91no—
211#946—92no—
212#938—91no—
213#935—92no—
214D4×Dic3—91no—
215#930—91no—
216#929—92no—
217C4×#67—91no—
218C4×#67—91no—
219C2×C4⋊Dic3—91no—
220#896—92no—
221#895—31no—
222#895—31no—
223#895—61no—
224#895—91no—
225#894—92no—
226#894—92no—
227#894—92no—
228#893—91no—
229D3×C4⋊C4—31no—
230D3×C4⋊C4—31no—
231D3×C4⋊C4—61no—
232D3×C4⋊C4—91no—
233D3×C4⋊C4—91no—
234#888—31no—
235#888—31no—
236#888—61no—
237#883—92no—
238#878—92no—
239C4×D12—91no—
240C4×D12—91no—
241C22×C3⋊D3C22×D312yes—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3⋊D3C22×D311yescharacteristic
244C22×C3×D3—31no—
245C22×C3×D3—31no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—61no—
251C22×C3×D3—61no—
252C22×C3×D3—62no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—22no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—41no—
260C2×C32×C4—42no—
261C2×C32×C4C22×D312yes—
262C2×C32×C4C22×D312yes—
263C2×C32×C4C22×D312yes—
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D312yes—
271C2×C3⋊Dic3C22×D312yes—
272C2×C3⋊Dic3C22×D311yescharacteristic
273C4⋊(C3⋊D3)—24no—
274C4⋊(C3⋊D3)—22no—
275C4×C3⋊D3—22no—
276C4×C3⋊D3—24no—
277C4×C3⋊D3—22no—
278#634—24no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—31no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—32no—
290C2×C3×Dic3—32no—
291C2×C3×Dic3—61no—
292C2×C3×Dic3—61no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—61no—
297C3×D12—64no—
298C3×D12—64no—
299C3×D12—62no—
300C3×D12—62no—
301C3×D12—122no—
302C3×D12—124no—
303C3×C4×D3—64no—
304C3×C4×D3—64no—
305C3×C4×D3—64no—
306C3×C4×D3—62no—
307C3×C4×D3—62no—
308C3×C4×D3—62no—
309C3×C4×D3—62no—
310C3×C4×D3—122no—
311C3×C4×D3—124no—
312C3×Dic6—64no—
313C3×Dic6—64no—
314C3×Dic6—124no—
315#626—34no—
316#626—34no—
317#626—64no—
318#626—64no—
319#625—34no—
320#625—64no—
321#624—64no—
322#624—64no—
323D3×Dic3—64no—
324D3×Dic3—64no—
325D3×Dic3—64no—
326D3×Dic3—64no—
327#547—271noSylow
328C2×C33C22×D411yescharacteristic
329C2×C33C2×#4111yescharacteristic
330C2×C332−1+411yescharacteristic
331C3×C3⋊D3—22no—
332C3×C3⋊D3—22no—
333C3×C3⋊D3—42no—
334C2×C3×Q8—92no—
335C2×C3×D4—91no—
336C2×C3×D4—92no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—92no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—92no—
343C2×#67—92no—
344C22×Dic3—92no—
345C22×Dic3—92no—
346#239—188no—
347#237—188no—
348#235—188no—
349C2×D12—31no—
350C2×D12—31no—
351C2×D12—32no—
352C2×D12—32no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—91no—
356C2×D12—92no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—32no—
360C2×C4×D3—32no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—62no—
365C2×C4×D3—61no—
366C2×C4×D3—92no—
367C2×C4×D3—92no—
368C2×C4×D3—92no—
369C2×C4×D3—92no—
370C2×Dic6—32no—
371C2×Dic6—32no—
372C2×Dic6—62no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—41no—
377C3×C4⋊C4—91no—
378C3×C4⋊C4—91no—
379C3×C4⋊C4—92no—
380C3×C4⋊C4—92no—
381C3×C4⋊C4D3211yescharacteristic
382C3×C4⋊C4D3211yescharacteristic
383C3×C4⋊C4D3211yescharacteristic
384C3×C22⋊C4—92no—
385C3×C42—91no—
386#217—92no—
387#217—92no—
388#217—91no—
389#217—91no—
390(C2×D3)⋊C4—32no—
391(C2×D3)⋊C4—32no—
392(C2×D3)⋊C4—62no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—92no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—91no—
397(C2×D3)⋊C4—92no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—92no—
400(C2×D3)⋊C4—92no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—91no—
408C4⋊Dic3—92no—
409Dic3⋊C4—32no—
410Dic3⋊C4—32no—
411Dic3⋊C4—32no—
412Dic3⋊C4—32no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—91no—
416Dic3⋊C4—92no—
417Dic3⋊C4—92no—
418Dic3⋊C4—91no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—41no—
426C22×C32C23×D311yescharacteristic
427C22×C32C23×D311yescharacteristic
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—21no—
433C2×C3⋊D3—22no—
434C2×C3⋊D3—22no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3D3×D412yes—
437C2×C3⋊D3D3×D412yes—
438C2×C3×D3—32no—
439C2×C3×D3—32no—
440C2×C3×D3—32no—
441C2×C3×D3—32no—
442C2×C3×D3—62no—
443C2×C3×D3—62no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—61no—
447C2×C3×D3—61no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—61no—
453C2×C3×D3—61no—
454C2×C3×D3—62no—
455C2×C3×D3—62no—
456C2×C3×D3—62no—
457C2×C3×D3—62no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—121no—
461C2×C3×D3—121no—
462C2×C3×D3—122no—
463C2×C3×D3—122no—
464C2×C3×D3—122no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—22no—
471C32×C4—42no—
472C32×C4—42no—
473C32×C4—42no—
474C32×C4—42no—
475C32×C4—82no—
476C32×C4#23512yescomplemented
477C32×C4#23712yescomplemented
478C32×C4#23912yescomplemented
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3—22no—
482C3⋊Dic3—22no—
483C3⋊Dic3—21no—
484C3⋊Dic3D3×D412yes—
485C3×Dic3—32no—
486C3×Dic3—32no—
487C3×Dic3—62no—
488C3×Dic3—62no—
489C3×Dic3—62no—
490C3×Dic3—61no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—122no—
501C3×Dic3—121no—
502C3×Dic3—122no—
503C2×#41—272no—
504C4⋊Q8—91no—
505#123—272no—
506#123—272no—
507C22⋊Q8—272no—
508#121—91no—
509#121—271no—
510C4×D4—271no—
511C4×D4—271no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—271no—
514C33#54711yescharacteristic, complemented, Sylow
515C23×C3—91no—
516C23×C3—91no—
517C23×C3—92no—
518C22×D3—31no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—31no—
522C22×D3—32no—
523C22×D3—32no—
524C22×D3—61no—
525C22×D3—61no—
526C22×D3—62no—
527C3×Q8—184no—
528C3×D4—184no—
529C3×D4—182no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—41no—
537C2×C3×C4—42no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—92no—
542C2×C3×C4—92no—
543C2×C3×C4—91no—
544C2×C3×C4—184no—
545C2×C3×C4—182no—
546C2×C3×C4—182no—
547C2×C3×C4C2×D3212yes—
548C2×C3×C4C2×D3212yes—
549C2×C3×C4C2×D3212yes—
550C2×C3×C4C2×D3211yescharacteristic
551C2×C3×C4C2×D3211yescharacteristic
552C2×C3×C4C2×D3211yescharacteristic
553#67—94no—
554#67—94no—
555#67—184no—
556#67—184no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—61no—
575C2×Dic3—184no—
576C2×Dic3—184no—
577D12—64no—
578D12—64no—
579D12—62no—
580D12—62no—
581D12—94no—
582D12—122no—
583D12—124no—
584D12—184no—
585C4×D3—64no—
586C4×D3—64no—
587C4×D3—64no—
588C4×D3—62no—
589C4×D3—62no—
590C4×D3—62no—
591C4×D3—62no—
592C4×D3—122no—
593C4×D3—124no—
594C4×D3—184no—
595C4×D3—184no—
596C4×D3—184no—
597C4×D3—184no—
598Dic6—64no—
599Dic6—64no—
600Dic6—124no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—41no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32C2×#23511yescharacteristic
614C2×C32C2×D3×D411yescharacteristic
615C2×C32C2×D3×D411yescharacteristic
616C2×C32C2×D3×D411yescharacteristic
617C2×C32C2×#23711yescharacteristic
618C2×C32C2×#23911yescharacteristic
619C2×C32#100711yescharacteristic
620C2×C32#100711yescharacteristic
621C2×C32#101011yescharacteristic
622C3⋊D3—22no—
623C3⋊D3—22no—
624C3⋊D3—42no—
625C3×D3—64no—
626C3×D3—62no—
627C3×D3—62no—
628C3×D3—62no—
629C3×D3—62no—
630C3×D3—122no—
631C3×D3—122no—
632C3×D3—122no—
633C3×D3—242no—
634#41—548no—
635C2×Q8—92no—
636C2×D4—91no—
637C2×D4—92no—
638C2×D4—271no—
639C2×D4—272no—
640C22×C4—91no—
641C22×C4—92no—
642C22×C4—91no—
643C22×C4—272no—
644C22×C4—272no—
645C4⋊C4—91no—
646C4⋊C4—92no—
647C4⋊C4—91no—
648C4⋊C4—92no—
649C4⋊C4—272no—
650C4⋊C4—271no—
651C4⋊C4#111311yescharacteristic
652C22⋊C4—92no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—272no—
656C22⋊C4—272no—
657C42—91no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—41no—
662C22×C3—92no—
663C22×C3—92no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3—182no—
669C22×C3—182no—
670C22×C3—182no—
671C22×C3C22×D3211yescharacteristic
672C22×C3C22×D3211yescharacteristic
673C22×C3C22×D3211yescharacteristic
674C2×D3—32no—
675C2×D3—32no—
676C2×D3—32no—
677C2×D3—32no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—62no—
691C2×D3—62no—
692C2×D3—62no—
693C2×D3—62no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—122no—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—82no—
712C3×C4—92no—
713C3×C4—181no—
714C3×C4—181no—
715C3×C4—182no—
716C3×C4—182no—
717C3×C4—181no—
718C3×C4#379512yescomplemented
719C3×C4#379612yescomplemented
720C3×C4#379912yescomplemented
721Dic3—32no—
722Dic3—32no—
723Dic3—62no—
724Dic3—62no—
725Dic3—62no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—62no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—61no—
735Dic3—61no—
736Dic3—122no—
737Dic3—121no—
738Dic3—122no—
739C32—21no—
740C32—21no—
741C32—21no—
742C32—41no—
743C32#550711yescharacteristic, complemented
744C32#561111yescharacteristic, complemented
745C32#572611yescharacteristic, complemented
746C23—91no—
747C23—91no—
748C23—92no—
749Q8—184no—
750D4—184no—
751D4—182no—
752D4—274no—
753D4—544no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—92no—
759C2×C4—92no—
760C2×C4—184no—
761C2×C4—182no—
762C2×C4—182no—
763C2×C4—544no—
764C2×C4—544no—
765C2×C4C2×#111312yes—
766C2×C4C2×#111311yescharacteristic
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—41no—
777C2×C3—41no—
778C2×C3—41no—
779C2×C3—182no—
780C2×C3—182no—
781C2×C3—362no—
782C2×C3C2×#379511yescharacteristic
783C2×C3C2×#379611yescharacteristic
784C2×C3C2×#379911yescharacteristic
785C2×C3D32×D411yescharacteristic
786C2×C3D32×D411yescharacteristic
787C2×C3D32×D411yescharacteristic
788C2×C3#6431511yescharacteristic
789C2×C3#6431511yescharacteristic
790C2×C3#6431611yescharacteristic
791D3—64no—
792D3—62no—
793D3—62no—
794D3—62no—
795D3—62no—
796D3—122no—
797D3—122no—
798D3—122no—
799D3—242no—
800C22—92no—
801C22—92no—
802C22—181no—
803C22—181no—
804C22—181no—
805C22—181no—
806C22—182no—
807C22—182no—
808C22—182no—
809C22C22×#111311yescharacteristic
810C4—22no—
811C4—92no—
812C4—181no—
813C4—181no—
814C4—182no—
815C4—182no—
816C4—181no—
817C4#8904112yescomplemented
818C3—21no—
819C3—21no—
820C3—21no—
821C3—41no—
822C3#1059437011yescharacteristic, complemented
823C3#1059437311yescharacteristic, complemented
824C3#1059451711yescharacteristic, complemented
825C2—182no—
826C2—182no—
827C2—362no—
828C2C2×#8904111yescharacteristic
829C2D4×#111311yescharacteristic
830C2#1172462411yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4#1113
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89041C2semidirect
2. C3×#64104C2semidirect
3. C3×C4⋊C4×C3⋊D3C2semidirect
4. C3×#64097C2semidirect
5. #11723696C2semidirect
6. #11723694C2semidirect
7. C4×#6295C2semidirect
8. #11723691C2semidirect
9. #11723689C2semidirect
10. #11723688C2semidirect
11. #11723686C2semidirect
42. #64104D3semidirect
43. C4⋊C4×C3⋊D3D3semidirect
44. #64097D3semidirect
93. #6295D4semidirect
198. C33×C4#41semidirect
476. C32×C4#235semidirect
477. C32×C4#237semidirect
478. C32×C4#239semidirect
514. C33#547semidirect
718. C3×C4#3795semidirect
719. C3×C4#3796semidirect
720. C3×C4#3799semidirect
743. C32#5507semidirect
744. C32#5611semidirect
745. C32#5726semidirect
817. C4#89041semidirect
822. C3#10594370semidirect
823. C3#10594373semidirect
824. C3#10594517semidirect

Maximal subgroups

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

subgroupindex
C2×#890412
C3×#641042
C3×C4⋊C4×C3⋊D32
C3×#640972
#117236962
#117236942
C4×#62952
#117236912
#117236892
#117236882
#117236862
#105945173
#105943733
#105943703