Finite Group Databasebeta

← #13175998

Subgroups — #13175998

Order 1728.

1892 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89021C211yesmaximal, characteristic
2C2×C3⋊D3×Dic6C211yesmaximal, characteristic, complemented
3#11723929C211yesmaximal, characteristic, complemented
4C3×#64103C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6#11723530C211yesmaximal, characteristic, complemented
7#11723528C211yesmaximal, characteristic, complemented
8#11723523C211yesmaximal, characteristic, complemented
9#11723518C211yesmaximal, characteristic, complemented
10#11723488C211yesmaximal, characteristic, complemented
11#11723483C211yesmaximal, characteristic, complemented
12#11723476C211yesmaximal, characteristic, complemented
13#11723466C211yesmaximal, characteristic, complemented
14#11723415C211yesmaximal, characteristic, complemented
15#11723395C211yesmaximal, characteristic, complemented
16#10596099—31nomaximal
17#10594365—34nomaximal
18C2×#6308C2211yescharacteristic
19C2×#6308C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31#89021—24no—
32C3⋊D3×Dic6—24no—
33C33×C4⋊C4C2211yescharacteristic
34C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic
35#88857C2211yescharacteristic
36#88857C2211yescharacteristic
37C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46#88807C2211yescharacteristic
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C2×#3828—31no—
57C2×#3795—34no—
58C2×D3×Dic6—34no—
59C32×C22⋊Q8—31no—
60#64155—31no—
61#64133—31no—
62#64106—31no—
63#64103—31no—
64#64103D311yescharacteristic, complemented
65#64101—31no—
66#64097—31no—
67#64097—31no—
68#64097—34no—
69#64097—64no—
70#64094—31no—
71#64094—31no—
72#64092—31no—
73#64092—31no—
74C3×#896D314yescomplemented
75C3×#894—34no—
76#63915—34no—
77#63913—34no—
78#63905—34no—
79#63893—34no—
80#63891—34no—
81#63887—34no—
82#63884—34no—
83#63878—34no—
84#63851—34no—
85#63840—34no—
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×D3C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96#6308—22no—
97#6308—22no—
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4⋊(C3⋊D3)—22no—
101C3×C4×C3⋊D3—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C32×C4×D3—22no—
106C32×Dic6—22no—
107#6293—22no—
108#6293—22no—
109#6290—22no—
110#6290—22no—
111Dic3×C3⋊D3—22no—
112Dic3×C3⋊D3—22no—
113Dic3×C3⋊D3D414yes—
114#5648—91no—
115#5628—94no—
116C2×C32×Q8—31no—
117C22×C32×C4—31no—
118C2×#638—31no—
119C2×#638—31no—
120Q8×C3⋊D3—64no—
121#3828—64no—
122C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
123C2×C4×C3⋊D3—31no—
124C2×C4×C3⋊D3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C4×C3⋊D3C2×D311yescharacteristic
127C2×#634—31no—
128C2×#634—31no—
129C2×#634—34no—
130C2×#634—34no—
131C2×#634—31no—
132C2×#634—31no—
133C2×#634—64no—
134C2×#634—64no—
135C2×C3×D12—34no—
136C2×C3×C4×D3—34no—
137C2×C3×C4×D3C2×D314yes—
138C2×C3×Dic6C2×D314yes—
139C2×#627—34no—
140C2×#627—34no—
141C2×#625—34no—
142C2×#625—34no—
143C2×D3×Dic3—34no—
144C2×D3×Dic3—34no—
145C2×D3×Dic3—34no—
146#3795—616no—
147D3×Dic6—616no—
148C32×C4⋊C4—24no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4C2×D314yes—
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C22⋊C4—31no—
154C32×C22⋊C4—31no—
155#3757—31no—
156#3757—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160#3752C2×D311yescharacteristic
161#3752C2×D311yescharacteristic
162#3752C2×D311yescharacteristic
163C4⋊(C3⋊Dic3)—31no—
164C4⋊(C3⋊Dic3)—34no—
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)—31no—
167C4⋊(C3⋊Dic3)—64no—
168#3750—31no—
169#3750—31no—
170#3750—34no—
171#3750—34no—
172#3750—31no—
173#3750—64no—
174#3750—64no—
175#3750C2×D311yescharacteristic
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—34no—
178C4×C3⋊Dic3—31no—
179C4×C3⋊Dic3—64no—
180C3×(C2×D3)⋊C4—34no—
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yes—
184C3×(C2×D3)⋊C4C2×D314yes—
185C3×Dic3⋊C4—34no—
186C3×Dic3⋊C4C2×D314yes—
187C3×Dic3⋊C4C2×D314yes—
188Dic3⋊Dic3—34no—
189Dic3⋊Dic3—34no—
190Dic3⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195(C2×D3)⋊Dic3—34no—
196Dic32—34no—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3C2×D412yes—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C33×C4—21no—
208C33×C4—21no—
209C33×C4—21no—
210C3⋊(C3⋊Dic3)—21no—
211C3⋊(C3⋊Dic3)—21no—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)C2×D412yes—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3C2×D412yes—
219C2×D3×Q8—94no—
220C2×#237—91no—
221C2×#235—94no—
222C22×Dic6—91no—
223C3×#123—91no—
224C3×C22⋊Q8—34no—
225#946—94no—
226#935—91no—
227#929—91no—
228#924—94no—
229#897—94no—
230#896—91no—
231#896C3⋊D311yescharacteristic, complemented
232#894—34no—
233#894—94no—
234#892—94no—
235#888—94no—
236#888—94no—
237#888—91no—
238#888—91no—
239#888—184no—
240#886—91no—
241#885—94no—
242#885—94no—
243#885—91no—
244#885—91no—
245#883—94no—
246#883—94no—
247#878—91no—
248#878—91no—
249#877—91no—
250C23×C32—31no—
251C22×C3⋊D3C22×D311yescharacteristic
252C22×C3⋊D3C22×D311yescharacteristic
253C22×C3×D3—34no—
254C22×C3×D3—34no—
255C22×C3×D3C22×D314yes—
256C32×Q8—62no—
257C2×C32×C4—24no—
258C2×C32×C4—24no—
259C2×C32×C4—24no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—62no—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D314yes—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270#638—62no—
271#638—62no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—34no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—34no—
280C2×C3⋊Dic3—64no—
281C2×C3⋊Dic3—64no—
282C2×C3⋊Dic3—64no—
283C2×C3⋊Dic3—64no—
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—22no—
287C4×C3⋊D3—22no—
288C4×C3⋊D3—34no—
289C4×C3⋊D3—62no—
290C4×C3⋊D3—62no—
291#634—62no—
292#634—62no—
293#634—62no—
294#634—62no—
295#634—68no—
296#634—68no—
297#634—128no—
298#634—128no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3C22×D314yes—
302C2×C3×Dic3C22×D314yes—
303C2×C3×Dic3C22×D314yes—
304C3×D12—68no—
305C3×C4×D3—28no—
306C3×C4×D3—68no—
307C3×Dic6—28no—
308#627—68no—
309#627—68no—
310#625—68no—
311#625—68no—
312D3×Dic3—316no—
313D3×Dic3—68no—
314D3×Dic3—68no—
315#536—271noSylow
316C2×C33C22×D411yescharacteristic
317C2×C332−1+411yescharacteristic
318C2×C332−1+411yescharacteristic
319C3×C3⋊D3—22no—
320C3×C3⋊D3—41no—
321C32×D3—41no—
322C2×C3×Q8—34no—
323C2×C3×D4—91no—
324C22×C3×C4—34no—
325C22×C3×C4—91no—
326C2×#67—94no—
327C2×#67—94no—
328C2×#67—91no—
329C2×#67—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333D3×Q8—1816no—
334#237—184no—
335#235—1816no—
336C2×D12—34no—
337C2×C4×D3—34no—
338C2×C4×D3—94no—
339C2×C4×D3—94no—
340C2×C4×D3—94no—
341C2×C4×D3C2×C3⋊D311yescharacteristic
342C2×Dic6—94no—
343C2×Dic6—94no—
344C2×Dic6—94no—
345C2×Dic6—94no—
346C2×Dic6—91no—
347C2×Dic6—91no—
348C2×Dic6—91no—
349C2×Dic6—91no—
350C2×Dic6—184no—
351C2×Dic6—184no—
352C2×Dic6—184no—
353C2×Dic6C2×C3⋊D311yescharacteristic
354C3×C4⋊C4—24no—
355C3×C4⋊C4—34no—
356C3×C4⋊C4—34no—
357C3×C4⋊C4—91no—
358C3×C4⋊C4D3214yes—
359C3×C4⋊C4C2×C3⋊D311yescharacteristic
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—91no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365#217—94no—
366#217—94no—
367#217—91no—
368#217—91no—
369#217—91no—
370(C2×D3)⋊C4—34no—
371(C2×D3)⋊C4—34no—
372(C2×D3)⋊C4—34no—
373(C2×D3)⋊C4—94no—
374(C2×D3)⋊C4—94no—
375(C2×D3)⋊C4—94no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
379(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
380C4⋊Dic3—94no—
381C4⋊Dic3—94no—
382C4⋊Dic3—94no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3—184no—
386Dic3⋊C4—34no—
387Dic3⋊C4—94no—
388Dic3⋊C4—94no—
389Dic3⋊C4—94no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—184no—
395Dic3⋊C4—184no—
396Dic3⋊C4C2×C3⋊D311yescharacteristic
397Dic3⋊C4C2×C3⋊D311yescharacteristic
398C4×Dic3—94no—
399C4×Dic3—94no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—184no—
403C22×C32—24no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32C23×D314yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—21no—
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3D3×D412yes—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—38no—
419C2×C3×D3—64no—
420C2×C3×D3—64no—
421C2×C3×D3—64no—
422C2×C3×D3—64no—
423C2×C3×D3—64no—
424C32×C4—28no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—21no—
429C32×C4—24no—
430C32×C4—24no—
431C32×C4—32no—
432C32×C4—44no—
433C32×C4—44no—
434C32×C4—61no—
435C32×C4—61no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—32no—
439C3⋊Dic3—38no—
440C3⋊Dic3—68no—
441C3⋊Dic3—68no—
442C3⋊Dic3—61no—
443C3⋊Dic3—61no—
444C3⋊Dic3—64no—
445C3⋊Dic3—61no—
446C3⋊Dic3—64no—
447C3⋊Dic3—64no—
448C3⋊Dic3—124no—
449C3⋊Dic3—124no—
450C3×Dic3—24no—
451C3×Dic3—24no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454C3×Dic3D3×D418yes—
455C2×#41—271no—
456C22×Q8—271no—
457C4⋊Q8—271no—
458C4⋊Q8—271no—
459#124—271no—
460#124—271no—
461#123—91no—
462#123—271no—
463#123—271no—
464#123—271no—
465C22⋊Q8—31no—
466C22⋊Q8—271no—
467C22⋊Q8—271no—
468C22⋊Q8—271no—
469#117—271no—
470C33#53611yescharacteristic, complemented, Sylow
471C23×C3—34no—
472C23×C3—91no—
473C23×C3—91no—
474C22×D3—34no—
475C22×D3—34no—
476C22×D3C22×C3⋊D311yescharacteristic
477C3×Q8—68no—
478C3×D4—182no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—34no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—68no—
486C2×C3×C4—91no—
487C2×C3×C4—91no—
488C2×C3×C4—182no—
489C2×C3×C4C2×D3214yes—
490C2×C3×C4C2×D3214yes—
491C2×C3×C4C2×D3214yes—
492C2×C3×C4C22×C3⋊D311yescharacteristic
493C2×C3×C4C22×C3⋊D311yescharacteristic
494C2×C3×C4C22×C3⋊D311yescharacteristic
495#67—182no—
496#67—188no—
497#67—182no—
498#67—188no—
499C2×Dic3—34no—
500C2×Dic3—34no—
501C2×Dic3—94no—
502C2×Dic3—91no—
503C2×Dic3—94no—
504C2×Dic3—94no—
505C2×Dic3—94no—
506C2×Dic3—94no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—184no—
511C2×Dic3—184no—
512C2×Dic3—184no—
513C2×Dic3—184no—
514C2×Dic3—182no—
515C2×Dic3—182no—
516C2×Dic3C22×C3⋊D311yescharacteristic
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519D12—68no—
520C4×D3—22no—
521C4×D3—68no—
522C4×D3—916no—
523C4×D3—188no—
524C4×D3—188no—
525Dic6—22no—
526Dic6—182no—
527Dic6—188no—
528Dic6—188no—
529Dic6—182no—
530Dic6—182no—
531Dic6—188no—
532Dic6—188no—
533Dic6—182no—
534Dic6—368no—
535Dic6—368no—
536C2×C32—24no—
537C2×C32—24no—
538C2×C32—24no—
539C2×C32—121no—
540C2×C32C2×D3×D414yes—
541C2×C32C2×D3×D411yescharacteristic
542C2×C32#100714yes—
543C2×C32#101014yes—
544C2×C32#101011yescharacteristic
545C2×C32#101011yescharacteristic
546C3⋊D3—22no—
547C3⋊D3—41no—
548C3×D3—44no—
549C3×D3—68no—
550C3×D3—124no—
551#41—544no—
552C2×Q8—31no—
553C2×Q8—271no—
554C2×Q8—271no—
555C2×Q8—271no—
556C2×Q8—271no—
557C2×Q8—544no—
558C2×D4—91no—
559C2×D4—271no—
560C2×D4—271no—
561C22×C4—31no—
562C22×C4—91no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—91no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C4⋊C4D3×C3⋊D311yescharacteristic
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—91no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C42—271no—
587C42—271no—
588C22×C3—24no—
589C22×C3—64no—
590C22×C3—64no—
591C22×C3—64no—
592C22×C3—92no—
593C22×C3—181no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3C22×D3214yes—
599C22×C3C23×C3⋊D311yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—38no—
604C2×D3—64no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C3×C4—28no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—24no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—38no—
617C3×C4—44no—
618C3×C4—44no—
619C3×C4—64no—
620C3×C4—64no—
621C3×C4—181no—
622C3×C4—181no—
623Dic3—21no—
624Dic3—21no—
625Dic3—64no—
626Dic3—64no—
627Dic3—98no—
628Dic3—92no—
629Dic3—188no—
630Dic3—188no—
631Dic3—184no—
632Dic3—184no—
633Dic3—184no—
634Dic3—181no—
635Dic3—181no—
636Dic3—181no—
637Dic3—364no—
638Dic3—364no—
639Dic3D4×C3⋊D312yes—
640C32—24no—
641C32#562814yescomplemented
642C32#564811yescharacteristic, complemented
643C23—31no—
644C23—91no—
645C23—91no—
646Q8—62no—
647Q8—542no—
648Q8—542no—
649Q8—542no—
650Q8—542no—
651D4—182no—
652D4—542no—
653D4—542no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—62no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—182no—
661C2×C4—274no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—542no—
667C2×C4—542no—
668C2×C4C2×D3×C3⋊D311yescharacteristic
669C2×C4C2×D3×C3⋊D311yescharacteristic
670C2×C4C2×D3×C3⋊D311yescharacteristic
671C2×C3—24no—
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—124no—
675C2×C3—182no—
676C2×C3—361no—
677C2×C3#6429814yes—
678C2×C3D32×D414yes—
679C2×C3#6431514yes—
680C2×C3C2×D4×C3⋊D311yescharacteristic
681C2×C3#6436411yescharacteristic
682C2×C3#6436711yescharacteristic
683D3—41no—
684D3—68no—
685D3—124no—
686C22—61no—
687C22—61no—
688C22—61no—
689C22—92no—
690C22—181no—
691C22—181no—
692C22—181no—
693C22—181no—
694C22—181no—
695C22C22×D3×C3⋊D311yescharacteristic
696C4—21no—
697C4—21no—
698C4—21no—
699C4—32no—
700C4—61no—
701C4—61no—
702C4—181no—
703C4—181no—
704C4—272no—
705C4—541no—
706C4—541no—
707C4—541no—
708C3—24no—
709C3#1059436514yescomplemented
710C3#1059609911yescharacteristic, complemented
711C2—121no—
712C2—182no—
713C2—361no—
714C2#1172456311yescharacteristic
715C2D3×D4×C3⋊D311yescharacteristic
716C2#1172459211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#89021C2
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#536
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊D3×Dic6C2semidirect
3. #11723929C2semidirect
4. C3×#64103C2semidirect
5. C32×#896C2semidirect
6. #11723530C2semidirect
7. #11723528C2semidirect
8. #11723523C2semidirect
9. #11723518C2semidirect
10. #11723488C2semidirect
11. #11723483C2semidirect
12. #11723476C2semidirect
13. #11723466C2semidirect
14. #11723415C2semidirect
15. #11723395C2semidirect
64. #64103D3semidirect
74. C3×#896D3semidirect
231. #896C3⋊D3semidirect
470. C33#536semidirect
641. C32#5628semidirect
642. C32#5648semidirect
709. C3#10594365semidirect
710. C3#10596099semidirect

Maximal subgroups

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

subgroupindex
C2×#890212
C2×C3⋊D3×Dic62
#117239292
C3×#641032
C32×#8962
#117235302
#117235282
#117235232
#117235182
#117234882
#117234832
#117234762
#117234662
#117234152
#117233952
#105960993
#105943653