Finite Group Databasebeta

← #13176471

Subgroups — #13176471

Order 1728.

2036 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89020C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
3#11723937C211yesmaximal, characteristic, complemented
4C3×#64102C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6#11723528C211yesmaximal, characteristic, complemented
7#11723520C211yesmaximal, characteristic, complemented
8#11723519C211yesmaximal, characteristic, complemented
9#11723506C211yesmaximal, characteristic, complemented
10#11723482C211yesmaximal, characteristic, complemented
11#11723472C211yesmaximal, characteristic, complemented
12#11723419C211yesmaximal, characteristic, complemented
13#11723418C211yesmaximal, characteristic, complemented
14#11723392C211yesmaximal, characteristic, complemented
15#11723390C211yesmaximal, characteristic, complemented
16#10596104—31nomaximal
17#10594375—34nomaximal
18C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34#89020—24no—
35C3⋊D3×Dic6—24no—
36C33×C4⋊C4C2211yescharacteristic
37#88859C2211yescharacteristic
38#88859C2211yescharacteristic
39#88857C2211yescharacteristic
40#88857C2211yescharacteristic
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic
43C3×C4×C3⋊Dic3C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48#88807C2211yescharacteristic
49#88804C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C2×#3828—31no—
57C2×#3798—34no—
58C2×D3×Dic6—34no—
59C32×C22⋊Q8—31no—
60#64156—31no—
61C4×#638—31no—
62#64105—31no—
63#64105—31no—
64#64105—34no—
65#64105—64no—
66#64104—31no—
67#64102—31no—
68#64102D311yescharacteristic, complemented
69#64096—31no—
70#64094—31no—
71#64094—31no—
72#64093—31no—
73#64093—31no—
74C3×#896D314yescomplemented
75C3×#893—34no—
76#63913—34no—
77#63907—34no—
78#63906—34no—
79#63886—34no—
80#63885—34no—
81#63881—34no—
82#63879—34no—
83#63852—34no—
84#63851—34no—
85#63837—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C4×C3⋊(C3⋊D3)—22no—
97#6308—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4⋊(C3⋊D3)—22no—
101C3×C4×C3⋊D3—22no—
102C3×C4×C3⋊D3—22no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×C4×D3—22no—
107C32×Dic6—22no—
108#6293—22no—
109#6293D414yescomplemented
110#6292—22no—
111#6292—22no—
112#6291—22no—
113#6290—22no—
114#6290—22no—
115Dic3×C3⋊D3—22no—
116Dic3×C3⋊D3—22no—
117#5633—94no—
118#5552—91no—
119C2×C32×Q8—31no—
120C22×C32×C4—31no—
121C2×#638—31no—
122C2×#638—31no—
123C2×#638—31no—
124Q8×C3⋊D3—64no—
125#3828—64no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—34no—
133C2×C4×C3⋊D3—64no—
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×C4×C3⋊D3C2×D311yescharacteristic
136C2×#634—31no—
137C2×#634—31no—
138C2×#634—34no—
139C2×#634—31no—
140C2×#634—64no—
141C2×C3×D12—34no—
142C2×C3×C4×D3—34no—
143C2×C3×C4×D3—34no—
144C2×C3×C4×D3C2×D314yes—
145C2×C3×Dic6C2×D314yes—
146C2×#627—34no—
147C2×#627—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#625—34no—
152C2×#625—34no—
153C2×D3×Dic3—34no—
154C2×D3×Dic3—34no—
155#3798—616no—
156D3×Dic6—616no—
157C32×C4⋊C4—24no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4C2×D314yes—
161C32×C4⋊C4C2×D311yescharacteristic
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164#3757—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—34no—
170#3752—34no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752C2×D311yescharacteristic
175#3752C2×D311yescharacteristic
176#3750—31no—
177#3750—31no—
178#3750—34no—
179#3750—34no—
180#3750—31no—
181#3750—64no—
182#3750—64no—
183C4×C3⋊Dic3—31no—
184C4×C3⋊Dic3—31no—
185C4×C3⋊Dic3C2×D311yescharacteristic
186C3×(C2×D3)⋊C4—34no—
187C3×(C2×D3)⋊C4—34no—
188C3×(C2×D3)⋊C4C2×D314yes—
189C3×(C2×D3)⋊C4C2×D314yes—
190C3×Dic3⋊C4C2×D314yes—
191C3×Dic3⋊C4C2×D314yes—
192C3×C4×Dic3—34no—
193Dic3⋊Dic3—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196(C2×D3)⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198Dic32—34no—
199Dic32—34no—
200C22×C33C2411yescharacteristic
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3#4112yescomplemented
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C33×C4—21no—
214C33×C4—21no—
215C33×C4—21no—
216C3⋊(C3⋊Dic3)—21no—
217C3⋊(C3⋊Dic3)—21no—
218C3⋊(C3⋊Dic3)C2×D412yes—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3C2×D412yes—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3C2×D412yes—
224C2×D3×Q8—94no—
225C2×#235—94no—
226C2×#235—91no—
227C22×Dic6—91no—
228C3×C22⋊Q8—34no—
229C3×C4×D4—91no—
230#947—94no—
231#939—91no—
232#939—91no—
233#930—91no—
234C4×#67—94no—
235#924—91no—
236#896—94no—
237#896—94no—
238#896—91no—
239#896—184no—
240#896C3⋊D311yescharacteristic, complemented
241#895—94no—
242#893—34no—
243#893—94no—
244#887—94no—
245#885—94no—
246#885—94no—
247#885—91no—
248#885—91no—
249#884—94no—
250#884—94no—
251#67⋊C4—91no—
252#67⋊C4—91no—
253#875—91no—
254C4×Dic6—91no—
255C23×C32—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—34no—
258C22×C3⋊D3—64no—
259C22×C3⋊D3C22×D311yescharacteristic
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3×D3—34no—
262C22×C3×D3—34no—
263C22×C3×D3C22×D314yes—
264C32×Q8—62no—
265C2×C32×C4—24no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—31no—
269C2×C32×C4—31no—
270C2×C32×C4—31no—
271C2×C32×C4—62no—
272C2×C32×C4C22×D314yes—
273C2×C32×C4C22×D314yes—
274C2×C32×C4C22×D314yes—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278#638—62no—
279#638—62no—
280#638—62no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—34no—
285C2×C3⋊Dic3—34no—
286C2×C3⋊Dic3—34no—
287C2×C3⋊Dic3—64no—
288C2×C3⋊Dic3—64no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3C22×D311yescharacteristic
291C2×C3⋊Dic3C22×D311yescharacteristic
292C4⋊(C3⋊D3)—22no—
293C4⋊(C3⋊D3)—62no—
294C4⋊(C3⋊D3)—62no—
295C4×C3⋊D3—22no—
296C4×C3⋊D3—22no—
297C4×C3⋊D3—62no—
298C4×C3⋊D3—62no—
299C4×C3⋊D3—62no—
300C4×C3⋊D3—68no—
301C4×C3⋊D3—128no—
302#634—34no—
303#634—62no—
304#634—62no—
305#634—68no—
306#634—128no—
307C2×C3×Dic3—34no—
308C2×C3×Dic3—34no—
309C2×C3×Dic3C22×D314yes—
310C2×C3×Dic3C22×D314yes—
311C2×C3×Dic3C22×D314yes—
312C3×D12—68no—
313C3×C4×D3—28no—
314C3×C4×D3—68no—
315C3×C4×D3—68no—
316C3×Dic6—28no—
317#627—316no—
318#627—68no—
319#626—68no—
320#626—68no—
321#626—68no—
322#625—68no—
323#625—68no—
324D3×Dic3—68no—
325D3×Dic3—68no—
326#548—271noSylow
327C2×C33C22×D411yescharacteristic
328C2×C33C2×#4111yescharacteristic
329C2×C332−1+411yescharacteristic
330C3⋊(C3⋊D3)—41no—
331C3×C3⋊D3—22no—
332C3×C3⋊D3—41no—
333C32×D3—41no—
334C2×C3×Q8—34no—
335C2×C3×D4—91no—
336C22×C3×C4—34no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C2×#67—94no—
340C2×#67—94no—
341C2×#67—94no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348D3×Q8—1816no—
349#235—184no—
350#235—1816no—
351C2×D12—34no—
352C2×D12—94no—
353C2×D12—94no—
354C2×D12—91no—
355C2×C4×D3—34no—
356C2×C4×D3—34no—
357C2×C4×D3—94no—
358C2×C4×D3—94no—
359C2×C4×D3—94no—
360C2×C4×D3—91no—
361C2×C4×D3—184no—
362C2×C4×D3C2×C3⋊D311yescharacteristic
363C2×Dic6—94no—
364C2×Dic6—91no—
365C2×Dic6—94no—
366C2×Dic6—94no—
367C2×Dic6—91no—
368C2×Dic6—91no—
369C2×Dic6—184no—
370C2×Dic6—184no—
371C2×Dic6C2×C3⋊D311yescharacteristic
372C3×C4⋊C4—24no—
373C3×C4⋊C4—34no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4D3214yes—
376C3×C4⋊C4C2×C3⋊D311yescharacteristic
377C3×C22⋊C4—34no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C42—91no—
382#217—94no—
383#217—91no—
384#217—91no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—94no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—94no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—184no—
397(C2×D3)⋊C4—184no—
398(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
399(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
400C4⋊Dic3—91no—
401Dic3⋊C4—94no—
402Dic3⋊C4—94no—
403Dic3⋊C4—94no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—184no—
407Dic3⋊C4—184no—
408Dic3⋊C4C2×C3⋊D311yescharacteristic
409Dic3⋊C4C2×C3⋊D311yescharacteristic
410C4×Dic3—34no—
411C4×Dic3—94no—
412C4×Dic3—94no—
413C4×Dic3—91no—
414C4×Dic3—91no—
415C22×C32—24no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32C23×D314yes—
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—21no—
422C2×C3⋊D3—21no—
423C2×C3⋊D3—21no—
424C2×C3⋊D3—21no—
425C2×C3⋊D3—21no—
426C2×C3⋊D3—68no—
427C2×C3⋊D3—61no—
428C2×C3⋊D3—61no—
429C2×C3⋊D3—64no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—64no—
432C2×C3⋊D3—64no—
433C2×C3⋊D3—124no—
434C2×C3⋊D3—124no—
435C2×C3⋊D3#23512yescomplemented
436C2×C3×D3—24no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—38no—
440C2×C3×D3—64no—
441C2×C3×D3—64no—
442C2×C3×D3—64no—
443C2×C3×D3—64no—
444C2×C3×D3—64no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—24no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—32no—
452C32×C4—44no—
453C32×C4—44no—
454C32×C4—44no—
455C32×C4—61no—
456C32×C4—61no—
457C3⋊Dic3—21no—
458C3⋊Dic3—32no—
459C3⋊Dic3—38no—
460C3⋊Dic3—68no—
461C3⋊Dic3—61no—
462C3⋊Dic3—61no—
463C3⋊Dic3—64no—
464C3⋊Dic3—64no—
465C3⋊Dic3—124no—
466C3⋊Dic3—124no—
467C3⋊Dic3D3×D412yes—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—38no—
471C3×Dic3—64no—
472C3×Dic3D3×D418yes—
473C2×#41—271no—
474C22×Q8—271no—
475#124—271no—
476#124—271no—
477#124—271no—
478C22⋊Q8—31no—
479C22⋊Q8—271no—
480C22⋊Q8—271no—
481#121—271no—
482#121—271no—
483#121—271no—
484C4×Q8—271no—
485C4×D4—91no—
486C4×D4—271no—
487C4×D4—271no—
488C33#54811yescharacteristic, complemented, Sylow
489C23×C3—34no—
490C23×C3—91no—
491C23×C3—91no—
492C22×D3—34no—
493C22×D3—34no—
494C22×D3—94no—
495C22×D3—91no—
496C22×D3—184no—
497C22×D3C22×C3⋊D311yescharacteristic
498C3×Q8—68no—
499C3×D4—182no—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—24no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—68no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—182no—
510C2×C3×C4—182no—
511C2×C3×C4C2×D3214yes—
512C2×C3×C4C2×D3214yes—
513C2×C3×C4C2×D3214yes—
514C2×C3×C4C22×C3⋊D311yescharacteristic
515C2×C3×C4C22×C3⋊D311yescharacteristic
516C2×C3×C4C22×C3⋊D311yescharacteristic
517#67—182no—
518#67—188no—
519#67—182no—
520#67—188no—
521#67—182no—
522#67—188no—
523#67—182no—
524C2×Dic3—34no—
525C2×Dic3—34no—
526C2×Dic3—94no—
527C2×Dic3—91no—
528C2×Dic3—94no—
529C2×Dic3—94no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—184no—
533C2×Dic3—184no—
534C2×Dic3—184no—
535C2×Dic3—182no—
536C2×Dic3—182no—
537C2×Dic3C22×C3⋊D311yescharacteristic
538C2×Dic3C22×C3⋊D311yescharacteristic
539C2×Dic3C22×C3⋊D311yescharacteristic
540D12—68no—
541D12—188no—
542D12—188no—
543D12—182no—
544C4×D3—22no—
545C4×D3—68no—
546C4×D3—68no—
547C4×D3—182no—
548C4×D3—188no—
549C4×D3—188no—
550C4×D3—188no—
551C4×D3—368no—
552Dic6—22no—
553Dic6—916no—
554Dic6—94no—
555Dic6—182no—
556Dic6—188no—
557Dic6—182no—
558Dic6—188no—
559Dic6—368no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—121no—
564C2×C32C2×#23511yescharacteristic
565C2×C32C2×D3×D414yes—
566C2×C32C2×D3×D411yescharacteristic
567C2×C32#100714yes—
568C2×C32D3×#4114yes—
569C2×C32#101011yescharacteristic
570C3⋊D3—22no—
571C3⋊D3—41no—
572C3⋊D3—128no—
573C3⋊D3—124no—
574C3⋊D3—121no—
575C3×D3—44no—
576C3×D3—68no—
577C3×D3—124no—
578#41—544no—
579C2×Q8—31no—
580C2×Q8—271no—
581C2×Q8—271no—
582C2×Q8—271no—
583C2×Q8—544no—
584C2×D4—91no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C22×C4—31no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—271no—
599C4⋊C4—271no—
600C4⋊C4—271no—
601C4⋊C4D3×C3⋊D311yescharacteristic
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—91no—
605C22⋊C4—91no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C42—91no—
613C42—271no—
614C42—271no—
615C22×C3—24no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—92no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3—181no—
625C22×C3C22×D3214yes—
626C22×C3C23×C3⋊D311yescharacteristic
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—38no—
631C2×D3—64no—
632C2×D3—64no—
633C2×D3—64no—
634C2×D3—64no—
635C2×D3—64no—
636C2×D3—188no—
637C2×D3—184no—
638C2×D3—184no—
639C2×D3—184no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—364no—
644C2×D3—364no—
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—24no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—38no—
652C3×C4—44no—
653C3×C4—44no—
654C3×C4—44no—
655C3×C4—64no—
656C3×C4—64no—
657C3×C4—92no—
658C3×C4—181no—
659Dic3—21no—
660Dic3—21no—
661Dic3—38no—
662Dic3—64no—
663Dic3—98no—
664Dic3—92no—
665Dic3—188no—
666Dic3—184no—
667Dic3—184no—
668Dic3—181no—
669Dic3—181no—
670Dic3—364no—
671Dic3—364no—
672Dic3D4×C3⋊D312yes—
673C32—24no—
674C32#555211yescharacteristic, complemented
675C32#563314yescomplemented
676C23—31no—
677C23—91no—
678C23—91no—
679C23—271no—
680Q8—62no—
681Q8—274no—
682Q8—542no—
683Q8—542no—
684D4—182no—
685D4—542no—
686D4—542no—
687D4—542no—
688D4—542no—
689D4—542no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—62no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—182no—
697C2×C4—182no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—271no—
701C2×C4—542no—
702C2×C4—542no—
703C2×C4—542no—
704C2×C4C2×D3×C3⋊D311yescharacteristic
705C2×C4C2×D3×C3⋊D311yescharacteristic
706C2×C4C2×D3×C3⋊D311yescharacteristic
707C2×C3—24no—
708C2×C3—24no—
709C2×C3—24no—
710C2×C3—124no—
711C2×C3—182no—
712C2×C3—361no—
713C2×C3D3×#23514yes—
714C2×C3D32×D414yes—
715C2×C3#6431514yes—
716C2×C3C2×D4×C3⋊D311yescharacteristic
717C2×C3#6436411yescharacteristic
718C2×C3#41×C3⋊D311yescharacteristic
719D3—41no—
720D3—68no—
721D3—124no—
722D3—368no—
723D3—361no—
724D3—364no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—92no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—541no—
735C22—541no—
736C22—541no—
737C22C22×D3×C3⋊D311yescharacteristic
738C4—21no—
739C4—21no—
740C4—21no—
741C4—32no—
742C4—61no—
743C4—61no—
744C4—92no—
745C4—181no—
746C4—272no—
747C4—541no—
748C4—541no—
749C3—24no—
750C3#1059437514yescomplemented
751C3#1059610411yescharacteristic, complemented
752C2—121no—
753C2—182no—
754C2—361no—
755C2—1081no—
756C2C3⋊D3×#23511yescharacteristic
757C2D3×D4×C3⋊D311yescharacteristic
758C2#1172459211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89020C2semidirect
2. C2×C3⋊D3×Dic6C2semidirect
3. #11723937C2semidirect
4. C3×#64102C2semidirect
5. C32×#896C2semidirect
6. #11723528C2semidirect
7. #11723520C2semidirect
8. #11723519C2semidirect
9. #11723506C2semidirect
10. #11723482C2semidirect
11. #11723472C2semidirect
12. #11723419C2semidirect
13. #11723418C2semidirect
14. #11723392C2semidirect
15. #11723390C2semidirect
68. #64102D3semidirect
74. C3×#896D3semidirect
109. #6293D4semidirect
209. C2×C3×C3⋊D3#41semidirect
240. #896C3⋊D3semidirect
435. C2×C3⋊D3#235semidirect
488. C33#548semidirect
674. C32#5552semidirect
675. C32#5633semidirect
750. C3#10594375semidirect
751. C3#10596104semidirect

Maximal subgroups

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

subgroupindex
C2×#890202
C2×C3⋊D3×Dic62
#117239372
C3×#641022
C32×#8962
#117235282
#117235202
#117235192
#117235062
#117234822
#117234722
#117234192
#117234182
#117233922
#117233902
#105961043
#105943753