Finite Group Databasebeta

← #13175337

Subgroups — #13175337

Order 1728.

1780 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊(C3⋊(C3⋊D3))C211yesmaximal, characteristic, complemented
2C3×#64081C211yesmaximal, characteristic, complemented
3C32×C4×Dic6C211yesmaximal, characteristic, complemented
4C4×#6292C211yesmaximal, characteristic, complemented
5C4×#6292C211yesmaximal, characteristic, complemented
6#11723504C211yesmaximal, characteristic, complemented
7#11723498C211yesmaximal, characteristic, complemented
8#11723486C211yesmaximal, characteristic
9#11723477C211yesmaximal, characteristic, complemented
10C4×#6289C211yesmaximal, characteristic, complemented
11#11723452C211yesmaximal, characteristic, complemented
12#11723411C211yesmaximal, characteristic, complemented
13#11723408C211yesmaximal, characteristic, complemented
14#11723400C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596051—31nomaximal
17#10593934—34nomaximal
18C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×#6292C2211yescharacteristic
24C2×#6292C2211yescharacteristic
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C33×C42C2211yescharacteristic
28#88859C2211yescharacteristic
29#88859C2211yescharacteristic
30C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×C4×C3⋊Dic3C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41#88806C2211yescharacteristic
42#88806C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic
52Dic3×C3⋊Dic3C2211yescharacteristic
53C32×C4×Q8—31no—
54#64156—31no—
55#64155—31no—
56#64107—31no—
57#64107—31no—
58#64104—31no—
59#64103—31no—
60#64103—31no—
61#64099—31no—
62C4×C4⋊(C3⋊D3)—31no—
63C4×C4⋊(C3⋊D3)—31no—
64C4×C4⋊(C3⋊D3)—31no—
65C4×C4⋊(C3⋊D3)—34no—
66C4×C4⋊(C3⋊D3)—64no—
67#64081—31no—
68#64081D311yescharacteristic, complemented
69C42×C3⋊D3—31no—
70C3×#872—34no—
71C3×C4×Dic6D314yescomplemented
72#63910—34no—
73#63907—34no—
74C4×#626—34no—
75C4×#626—34no—
76#63897—34no—
77#63888—34no—
78C4×#624—34no—
79#63874—34no—
80#63861—34no—
81#63854—34no—
82#63848—34no—
83#63845—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
91C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
92C4⋊(C3⋊(C3⋊D3))—22no—
93C4×C3⋊(C3⋊D3)—22no—
94C4×C3⋊(C3⋊D3)—22no—
95C2×C3×C3⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C3×C4×C3⋊D3—22no—
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×Dic6—22no—
104#6292—22no—
105#6292—22no—
106#6289—22no—
107#6289—22no—
108#5580—94no—
109#5528—91no—
110C2×C32×Q8—31no—
111C2×C4⋊(C3⋊D3)—31no—
112C2×C4⋊(C3⋊D3)—31no—
113C2×C4⋊(C3⋊D3)—31no—
114C2×C4⋊(C3⋊D3)—34no—
115C2×C4⋊(C3⋊D3)—64no—
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—34no—
119C2×C4×C3⋊D3—34no—
120C2×C4×C3⋊D3—31no—
121C2×C4×C3⋊D3—31no—
122C2×C4×C3⋊D3—64no—
123C2×C4×C3⋊D3—64no—
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×C3×C4×D3—34no—
126C2×C3×Dic6C2×D314yes—
127C2×#626—34no—
128C2×#626—34no—
129C2×#624—34no—
130C2×#624—34no—
131C32×C4⋊C4—31no—
132C32×C4⋊C4—31no—
133C32×C4⋊C4—31no—
134C32×C42—24no—
135C32×C42—31no—
136C32×C42—31no—
137C32×C42C2×D314yes—
138C32×C42C2×D311yescharacteristic
139#3752—31no—
140#3752—31no—
141#3752—31no—
142#3752—31no—
143#3752—34no—
144#3752—34no—
145#3752—31no—
146#3752—31no—
147#3752—31no—
148#3752—31no—
149#3752—64no—
150#3752—64no—
151#3752C2×D311yescharacteristic
152#3752C2×D311yescharacteristic
153C4⋊(C3⋊Dic3)—31no—
154C4⋊(C3⋊Dic3)—34no—
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—64no—
158#3750—31no—
159#3750—31no—
160#3750C2×D311yescharacteristic
161#3750C2×D311yescharacteristic
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3C2×D311yescharacteristic
165C3×(C2×D3)⋊C4—34no—
166C3×(C2×D3)⋊C4—34no—
167C3×C4⋊Dic3C2×D314yes—
168C3×Dic3⋊C4—34no—
169C3×Dic3⋊C4—34no—
170C3×Dic3⋊C4C2×D314yes—
171C3×Dic3⋊C4C2×D314yes—
172C3×C4×Dic3—34no—
173C3×C4×Dic3C2×D314yes—
174C3×C4×Dic3C2×D314yes—
175#3724—34no—
176#3724—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179#3722—34no—
180#3722—34no—
181#3722—34no—
182#3722—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185Dic32—34no—
186Dic32—34no—
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)—21no—
193C2×C3⋊(C3⋊D3)#4112yes—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4#4112yes—
200C3⋊(C3⋊Dic3)—21no—
201C3⋊(C3⋊Dic3)—21no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3#4112yes—
209C3×C4×Q8—34no—
210C3×#117—91no—
211#947—94no—
212#946—94no—
213C4×#67—91no—
214C4×#67—91no—
215#898—94no—
216#898—94no—
217#898—91no—
218#896—91no—
219#895—94no—
220#894—94no—
221#894—94no—
222#894—91no—
223#890—94no—
224#889—91no—
225#885—91no—
226#884—91no—
227#883—91no—
228#879—91no—
229C4×D12—94no—
230C4×D12—94no—
231C4×D12—94no—
232C4×D12—91no—
233C4×D12—184no—
234#872—34no—
235#872—94no—
236#872—91no—
237C42×D3—94no—
238C42×D3—91no—
239C4×Dic6C3⋊D311yescharacteristic, complemented
240C22×C3⋊D3—31no—
241C22×C3⋊D3—31no—
242C22×C3⋊D3—34no—
243C22×C3⋊D3—34no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—64no—
246C22×C3⋊D3C22×D311yescharacteristic
247C22×C3×D3—34no—
248C32×Q8—62no—
249C2×C32×C4—24no—
250C2×C32×C4—24no—
251C2×C32×C4—24no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4—31no—
256C2×C32×C4C22×D314yes—
257C2×C32×C4C22×D314yes—
258C2×C32×C4C22×D314yes—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—34no—
265C2×C3⋊Dic3—34no—
266C2×C3⋊Dic3—64no—
267C2×C3⋊Dic3—64no—
268C2×C3⋊Dic3C22×D311yescharacteristic
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D311yescharacteristic
271C4⋊(C3⋊D3)—62no—
272C4⋊(C3⋊D3)—68no—
273C4⋊(C3⋊D3)—616no—
274C4⋊(C3⋊D3)—62no—
275C4⋊(C3⋊D3)—62no—
276C4×C3⋊D3—22no—
277C4×C3⋊D3—62no—
278C4×C3⋊D3—62no—
279C4×C3⋊D3—62no—
280C4×C3⋊D3—62no—
281C4×C3⋊D3—68no—
282C4×C3⋊D3—68no—
283C4×C3⋊D3—128no—
284C4×C3⋊D3—128no—
285C2×C3×Dic3—34no—
286C2×C3×Dic3—34no—
287C2×C3×Dic3—34no—
288C2×C3×Dic3C22×D314yes—
289C2×C3×Dic3C22×D314yes—
290C2×C3×Dic3C22×D314yes—
291C2×C3×Dic3C22×D314yes—
292C3×C4×D3—68no—
293C3×Dic6—28no—
294#626—68no—
295#626—68no—
296#624—68no—
297#624—68no—
298#529—271noSylow
299C2×C33C2×#4111yescharacteristic
300C2×C33C2×#4111yescharacteristic
301C2×C33C2×#4111yescharacteristic
302C3⋊(C3⋊D3)—22no—
303C3⋊(C3⋊D3)—41no—
304C3×C3⋊D3—41no—
305C2×C3×Q8—34no—
306C22×C3×C4—91no—
307C2×#67—91no—
308C2×#67—91no—
309C2×D12—94no—
310C2×D12—94no—
311C2×D12—94no—
312C2×D12—91no—
313C2×D12—184no—
314C2×C4×D3—34no—
315C2×C4×D3—94no—
316C2×C4×D3—94no—
317C2×C4×D3—94no—
318C2×C4×D3—94no—
319C2×C4×D3—91no—
320C2×C4×D3—91no—
321C2×C4×D3—91no—
322C2×C4×D3—91no—
323C2×C4×D3—184no—
324C2×C4×D3—184no—
325C2×Dic6C2×C3⋊D311yescharacteristic
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4—91no—
333C3×C42—24no—
334C3×C42—34no—
335C3×C42—34no—
336C3×C42—91no—
337C3×C42D3214yes—
338C3×C42C2×C3⋊D311yescharacteristic
339#217—91no—
340#217—91no—
341(C2×D3)⋊C4—34no—
342(C2×D3)⋊C4—34no—
343(C2×D3)⋊C4—94no—
344(C2×D3)⋊C4—94no—
345(C2×D3)⋊C4—94no—
346(C2×D3)⋊C4—94no—
347(C2×D3)⋊C4—94no—
348(C2×D3)⋊C4—94no—
349(C2×D3)⋊C4—94no—
350(C2×D3)⋊C4—94no—
351(C2×D3)⋊C4—91no—
352(C2×D3)⋊C4—91no—
353(C2×D3)⋊C4—91no—
354(C2×D3)⋊C4—91no—
355(C2×D3)⋊C4—91no—
356(C2×D3)⋊C4—91no—
357(C2×D3)⋊C4—184no—
358(C2×D3)⋊C4—184no—
359C4⋊Dic3—94no—
360C4⋊Dic3—94no—
361C4⋊Dic3—94no—
362C4⋊Dic3—91no—
363C4⋊Dic3—184no—
364C4⋊Dic3C2×C3⋊D311yescharacteristic
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—94no—
368Dic3⋊C4—94no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4C2×C3⋊D311yescharacteristic
374Dic3⋊C4C2×C3⋊D311yescharacteristic
375C4×Dic3—34no—
376C4×Dic3—94no—
377C4×Dic3—94no—
378C4×Dic3—91no—
379C4×Dic3—91no—
380C4×Dic3C2×C3⋊D311yescharacteristic
381C4×Dic3C2×C3⋊D311yescharacteristic
382C22×C32—24no—
383C22×C32C23×D314yes—
384C22×C32C23×D311yescharacteristic
385C2×C3⋊D3—21no—
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—32no—
389C2×C3⋊D3—38no—
390C2×C3⋊D3—68no—
391C2×C3⋊D3—61no—
392C2×C3⋊D3—61no—
393C2×C3⋊D3—68no—
394C2×C3⋊D3—61no—
395C2×C3⋊D3—64no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—64no—
399C2×C3⋊D3—64no—
400C2×C3⋊D3—64no—
401C2×C3⋊D3—64no—
402C2×C3⋊D3—124no—
403C2×C3⋊D3—124no—
404C2×C3⋊D3—124no—
405C2×C3⋊D3—124no—
406C2×C3×D3—64no—
407C2×C3×D3—64no—
408C2×C3×D3—64no—
409C32×C4—28no—
410C32×C4—24no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—28no—
414C32×C4—24no—
415C32×C4—32no—
416C32×C4—44no—
417C32×C4—61no—
418C32×C4—61no—
419C32×C4—61no—
420C32×C4#23512yes—
421C32×C4#23918yes—
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3⋊Dic3—64no—
428C3⋊Dic3—64no—
429C3⋊Dic3—124no—
430C3⋊Dic3—124no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C3×Dic3—24no—
434C3×Dic3—64no—
435C3×Dic3—64no—
436C3×Dic3—64no—
437C3×Dic3#23518yes—
438#126—271no—
439#126—271no—
440#125—271no—
441#124—271no—
442#123—271no—
443#123—271no—
444C22⋊Q8—271no—
445#121—271no—
446C4×Q8—31no—
447C4×D4—271no—
448C4×D4—271no—
449C4×D4—271no—
450#117—91no—
451#117—271no—
452C2×C42—271no—
453C33#52911yescharacteristic, complemented, Sylow
454C23×C3—91no—
455C22×D3—34no—
456C22×D3—94no—
457C22×D3—91no—
458C22×D3—94no—
459C22×D3—91no—
460C22×D3—184no—
461C22×D3—184no—
462C3×Q8—68no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—91no—
471C2×C3×C4—91no—
472C2×C3×C4—91no—
473C2×C3×C4—182no—
474C2×C3×C4C2×D3214yes—
475C2×C3×C4C2×D3214yes—
476C2×C3×C4C2×D3214yes—
477C2×C3×C4C22×C3⋊D311yescharacteristic
478C2×C3×C4C22×C3⋊D311yescharacteristic
479C2×C3×C4C22×C3⋊D311yescharacteristic
480#67—182no—
481#67—182no—
482C2×Dic3—34no—
483C2×Dic3—34no—
484C2×Dic3—34no—
485C2×Dic3—94no—
486C2×Dic3—94no—
487C2×Dic3—91no—
488C2×Dic3—91no—
489C2×Dic3—184no—
490C2×Dic3—184no—
491C2×Dic3C22×C3⋊D311yescharacteristic
492C2×Dic3C22×C3⋊D311yescharacteristic
493C2×Dic3C22×C3⋊D311yescharacteristic
494C2×Dic3C22×C3⋊D311yescharacteristic
495D12—188no—
496D12—182no—
497D12—1816no—
498D12—188no—
499D12—188no—
500C4×D3—68no—
501C4×D3—182no—
502C4×D3—188no—
503C4×D3—188no—
504C4×D3—188no—
505C4×D3—188no—
506C4×D3—182no—
507C4×D3—182no—
508C4×D3—182no—
509C4×D3—368no—
510C4×D3—368no—
511Dic6—22no—
512C2×C32—24no—
513C2×C32—24no—
514C2×C32—24no—
515C2×C32C2×#23514yes—
516C2×C32C2×#23511yescharacteristic
517C2×C32C2×#23914yes—
518C2×C32D3×#4114yes—
519C2×C32D3×#4111yescharacteristic
520C2×C32D3×#4111yescharacteristic
521C3⋊D3—41no—
522C3⋊D3—62no—
523C3⋊D3—68no—
524C3⋊D3—128no—
525C3⋊D3—128no—
526C3⋊D3—121no—
527C3⋊D3—124no—
528C3×D3—124no—
529C2×Q8—31no—
530C2×D4—271no—
531C2×D4—271no—
532C2×D4—271no—
533C22×C4—91no—
534C22×C4—271no—
535C22×C4—271no—
536C22×C4—271no—
537C22×C4—271no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C4⋊C4—271no—
547C4⋊C4—271no—
548C22⋊C4—91no—
549C22⋊C4—91no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4—271no—
557C22⋊C4—271no—
558C42—31no—
559C42—31no—
560C42—91no—
561C42—271no—
562C42—271no—
563C42D3×C3⋊D311yescharacteristic
564C22×C3—24no—
565C22×C3—181no—
566C22×C3—181no—
567C22×C3—181no—
568C22×C3C22×D3214yes—
569C22×C3C23×C3⋊D311yescharacteristic
570C2×D3—64no—
571C2×D3—64no—
572C2×D3—64no—
573C2×D3—98no—
574C2×D3—92no—
575C2×D3—188no—
576C2×D3—184no—
577C2×D3—184no—
578C2×D3—181no—
579C2×D3—181no—
580C2×D3—188no—
581C2×D3—184no—
582C2×D3—184no—
583C2×D3—184no—
584C2×D3—181no—
585C2×D3—181no—
586C2×D3—181no—
587C2×D3—364no—
588C2×D3—364no—
589C2×D3—364no—
590C2×D3—364no—
591C3×C4—28no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—28no—
597C3×C4—38no—
598C3×C4—44no—
599C3×C4—64no—
600C3×C4—64no—
601C3×C4—64no—
602C3×C4—181no—
603C3×C4—181no—
604C3×C4—181no—
605C3×C4#379918yes—
606C3×C4#383212yes—
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—64no—
611Dic3—64no—
612Dic3—64no—
613Dic3—184no—
614Dic3—184no—
615Dic3—181no—
616Dic3—181no—
617Dic3—364no—
618Dic3—364no—
619Dic3#382812yes—
620C32—24no—
621C32#552811yescharacteristic, complemented
622C32#558014yescomplemented
623C23—91no—
624C23—271no—
625C23—271no—
626Q8—62no—
627D4—542no—
628D4—542no—
629D4—542no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—91no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—182no—
638C2×C4—271no—
639C2×C4—271no—
640C2×C4—542no—
641C2×C4—542no—
642C2×C4—542no—
643C2×C4—542no—
644C2×C4C2×D3×C3⋊D311yescharacteristic
645C2×C4C2×D3×C3⋊D311yescharacteristic
646C2×C4C2×D3×C3⋊D311yescharacteristic
647C2×C3—24no—
648C2×C3—24no—
649C2×C3—24no—
650C2×C3—361no—
651C2×C3C2×#379914yes—
652C2×C3D3×#23514yes—
653C2×C3#6430614yes—
654C2×C3C2×#382811yescharacteristic
655C2×C3C2×#383211yescharacteristic
656C2×C3#41×C3⋊D311yescharacteristic
657D3—124no—
658D3—188no—
659D3—182no—
660D3—368no—
661D3—368no—
662D3—364no—
663D3—361no—
664C22—181no—
665C22—181no—
666C22—181no—
667C22—272no—
668C22—541no—
669C22—541no—
670C22—541no—
671C22—541no—
672C22—541no—
673C22C22×D3×C3⋊D311yescharacteristic
674C4—21no—
675C4—21no—
676C4—32no—
677C4—61no—
678C4—61no—
679C4—61no—
680C4—181no—
681C4—181no—
682C4—181no—
683C4—541no—
684C4—541no—
685C4#8901812yes—
686C3—24no—
687C3#1059393414yescomplemented
688C3#1059605111yescharacteristic, complemented
689C2—361no—
690C2—542no—
691C2—1081no—
692C2C2×#8901811yescharacteristic
693C2D3×#382811yescharacteristic
694C2#1172457811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
prime radical#11723486C2
hypercenterC42D3×C3⋊D3
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊(C3⋊(C3⋊D3))C2semidirect
2. C3×#64081C2semidirect
3. C32×C4×Dic6C2semidirect
4. C4×#6292C2semidirect
5. C4×#6292C2semidirect
6. #11723504C2semidirect
7. #11723498C2semidirect
9. #11723477C2semidirect
10. C4×#6289C2semidirect
11. #11723452C2semidirect
12. #11723411C2semidirect
13. #11723408C2semidirect
14. #11723400C2semidirect
15. #11723392C2semidirect
68. #64081D3semidirect
71. C3×C4×Dic6D3semidirect
239. C4×Dic6C3⋊D3semidirect
453. C33#529semidirect
621. C32#5528semidirect
622. C32#5580semidirect
687. C3#10593934semidirect
688. C3#10596051semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊(C3⋊(C3⋊D3))2
C3×#640812
C32×C4×Dic62
C4×#62922
#117235042
#117234982
#117234862
#117234772
C4×#62892
#117234522
#117234112
#117234082
#117234002
#117233922
#105960513
#105939343