Finite Group Databasebeta

← #11824507

Subgroups — #11824507

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic, complemented
2C2×#63904C211yesmaximal, characteristic
3C2×#63895C211yesmaximal, characteristic, complemented
4C2×#63888C211yesmaximal, characteristic, complemented
5C2×#63851C211yesmaximal, characteristic, complemented
6C2×#63839C211yesmaximal, characteristic, complemented
7#10592692C211yesmaximal, characteristic, complemented
8C3×#4975C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic
10#10591383C211yesmaximal, characteristic
11#10591324C211yesmaximal, characteristic, complemented
12#10591303C211yesmaximal, characteristic, complemented
13#10591244C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#10591203C211yesmaximal, characteristic, complemented
16#82780—31nomaximal
17#74334—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#896—24no—
40C2×#3724C2211yescharacteristic
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×Dic32C2211yescharacteristic
51C2×Dic32C2211yescharacteristic
52#63904—24no—
53#63895—24no—
54#63888—24no—
55#63851—24no—
56#63839—24no—
57#63658C2211yescharacteristic
58#63579C2211yescharacteristic
59C2×C3×C22⋊Q8—31no—
60C2×#946—31no—
61C2×#944—31no—
62C2×C4×#67—31no—
63C2×#924—31no—
64C2×#897—31no—
65C2×#896—31no—
66C2×#896—31no—
67C2×#896—31no—
68C2×#896D311yescharacteristic, complemented
69C2×#893—31no—
70C2×#888—31no—
71C3×#384—31no—
72#4993—31no—
73#4993—31no—
74#4993—31no—
75#4993—31no—
76#4993—31no—
77#4993—31no—
78#4993—61no—
79#4988—31no—
80#4975—31no—
81#4975—31no—
82#4975D311yescharacteristic, complemented
83Dic3×C4⋊C4—31no—
84#4957—31no—
85#4957—31no—
86#4949—31no—
87#4949—31no—
88#4939—31no—
89C4×Dic3⋊C4—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—22no—
110C2×C3×Dic6—22no—
111C2×#627—22no—
112C2×#627—22no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#626Q814yescomplemented
117C2×#624—22no—
118C2×#624—22no—
119C2×#624—22no—
120C32×C4⋊C4—22no—
121#3752—22no—
122#3752—22no—
123#3752—22no—
124#3750—22no—
125#3750—22no—
126C3×(C2×D3)⋊C4—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×C4⋊Dic3—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4D414yescomplemented
135C3×C4×Dic3—22no—
136#3724—22no—
137#3724—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3D414yescomplemented
141#3722—22no—
142#3722—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146Dic32—22no—
147Dic32D414yes—
148#2542—91noSylow
149C22×C3×Q8—31no—
150C23×C3×C4—31no—
151C22×#67—31no—
152C22×D12—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3C2×D311yescharacteristic
156C22×Dic6—31no—
157C22×Dic6—31no—
158C22×Dic6C2×D311yescharacteristic
159C3×C22⋊Q8—64no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C42—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176#946—64no—
177#944—64no—
178C4×#67—64no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4—61no—
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3C2×D311yescharacteristic
201#924—64no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—61no—
214C2×Dic3⋊C4—61no—
215C2×Dic3⋊C4C2×D311yescharacteristic
216C2×Dic3⋊C4C2×D311yescharacteristic
217C2×Dic3⋊C4C2×D311yescharacteristic
218C2×Dic3⋊C4C2×D311yescharacteristic
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3C2×D311yescharacteristic
226#897—64no—
227#896—24no—
228#896—64no—
229#896—64no—
230#896—64no—
231#893—64no—
232#888—64no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—61no—
238C23×C32C2411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3⋊D3—21no—
245C22×C3⋊D3C2×Q812yes—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3C2×Q812yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4C2×D412yes—
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⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×D412yes—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D412yes—
285C2×C3×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×Q812yes—
291C2×C3×Dic3#4112yes—
292C3×C4×D3—44no—
293C3×Dic6—44no—
294#627—44no—
295#626—28no—
296#624—44no—
297C2×C4⋊Q8—91no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8—91no—
300C2×C22⋊Q8—91no—
301C2×C22⋊Q8—91no—
302C2×C4×D4—91no—
303#399—91no—
304#399—91no—
305#399—91no—
306#399—91no—
307#390—91no—
308#390—91no—
309#384—31no—
310#384—91no—
311C4×C4⋊C4—91no—
312C24×C3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—61no—
316C23×D3C22×D311yescharacteristic
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8—62no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—34no—
340C2×#67—62no—
341C2×#67—62no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—61no—
349C22×Dic3—61no—
350C22×Dic3—61no—
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×D12—34no—
359C2×D12—62no—
360C2×D12—62no—
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3—22no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—62no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×Dic6—22no—
371C2×Dic6—22no—
372C2×Dic6—22no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—42no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C4⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C42—62no—
392#217—62no—
393#217—62no—
394#217—62no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—62no—
398(C2×D3)⋊C4—62no—
399(C2×D3)⋊C4—62no—
400(C2×D3)⋊C4—62no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—122no—
411(C2×D3)⋊C4—122no—
412(C2×D3)⋊C4—122no—
413C4⋊Dic3—22no—
414C4⋊Dic3—34no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—34no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—122no—
434Dic3⋊C4—122no—
435Dic3⋊C4#6714yescomplemented
436C4×Dic3—22no—
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32C22×D411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C22×D411yescharacteristic
444C22×C32C22×Q811yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C322−1+411yescharacteristic
447C22×C322−1+411yescharacteristic
448C2×C3⋊D3—22no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—41no—
464C32×C4—41no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C22⋊Q814yescomplemented
474C3×Dic3#12714yes—
475C22×Q8—31no—
476C22×Q8—91no—
477C22×D4—91no—
478C23×C4—31no—
479C23×C4—91no—
480C4⋊Q8—184no—
481C22⋊Q8—64no—
482C22⋊Q8—184no—
483C22⋊Q8—184no—
484C22⋊Q8—184no—
485C4×D4—184no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4D3211yescharacteristic
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C42—31no—
512C2×C42—91no—
513C2×C42—91no—
514#95—91no—
515#95—91no—
516C23×C3—21no—
517C23×C3—32no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3C23×D311yescharacteristic
525C23×C3C23×D311yescharacteristic
526C22×D3—21no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—62no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3—121no—
551C22×D3—121no—
552C22×D3—121no—
553C22×D3D3×Q812yes—
554C3×Q8—124no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—124no—
602C2×C3×C4D3×D412yes—
603C2×C3×C4C2×#6712yes—
604#67—68no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3#23512yes—
646C2×Dic3D3×D412yes—
647C2×Dic3D3×D412yes—
648C2×Dic3D3×D412yes—
649C2×Dic3D3×D412yes—
650C2×Dic3D3×Q812yes—
651C2×Dic3C2×#6712yes—
652C2×Dic3C2×#6712yes—
653D12—68no—
654C4×D3—44no—
655C4×D3—124no—
656C4×D3—124no—
657Dic6—44no—
658Dic6—124no—
659Dic6—124no—
660C2×C32C2×C22⋊Q811yescharacteristic
661C2×C32C2×#12711yescharacteristic
662C2×C32#53611yescharacteristic
663C2×C32#54711yescharacteristic
664C2×C32#54711yescharacteristic
665C2×C32D4×Q811yescharacteristic
666C2×C32D4×Q811yescharacteristic
667C3⋊D3—42no—
668C3×D3—42no—
669C24—31no—
670C24—91no—
671C2×Q8—62no—
672C2×Q8—62no—
673C2×Q8—62no—
674C2×Q8—182no—
675C2×Q8—182no—
676C2×Q8—182no—
677C2×D4—94no—
678C2×D4—182no—
679C2×D4—182no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—182no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4C2×D3211yescharacteristic
697C22×C4C2×D3211yescharacteristic
698C22×C4C2×D3211yescharacteristic
699C4⋊C4—22no—
700C4⋊C4—34no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—94no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—182no—
717C22⋊C4—182no—
718C22⋊C4—182no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C42—62no—
725C42—94no—
726C42—182no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3C2×#23511yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C22×C3C2×D3×D411yescharacteristic
744C22×C3C2×D3×D411yescharacteristic
745C22×C3C2×D3×D411yescharacteristic
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×Q811yescharacteristic
748C22×C3C2×D3×Q811yescharacteristic
749C22×C3#100711yescharacteristic
750C22×C3#100711yescharacteristic
751C22×C3#100711yescharacteristic
752C22×C3D3×#4111yescharacteristic
753C22×C3#101011yescharacteristic
754C22×C3C22×#6711yescharacteristic
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—34no—
786C3×C4—34no—
787C3×C4—42no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—81no—
795C3×C4—81no—
796C3×C4—121no—
797C3×C4—121no—
798C3×C4—121no—
799Dic3—22no—
800Dic3—22no—
801Dic3—41no—
802Dic3—41no—
803Dic3—41no—
804Dic3—62no—
805Dic3—62no—
806Dic3—62no—
807Dic3—62no—
808Dic3—122no—
809Dic3—122no—
810Dic3—121no—
811Dic3—121no—
812Dic3—241no—
813Dic3#89614yescomplemented
814Dic3#94014yes—
815C32#254211yescharacteristic, complemented, Sylow
816C23—32no—
817C23—61no—
818C23—61no—
819C23—61no—
820C23—61no—
821C23—61no—
822C23—61no—
823C23—92no—
824C23—181no—
825C23—181no—
826C23—181no—
827C23—181no—
828C23—181no—
829C23—181no—
830C23C22×D3211yescharacteristic
831Q8—124no—
832Q8—364no—
833D4—188no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—32no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—124no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—364no—
874C2×C4D3×#6712yes—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—122no—
883C2×C3#550711yescharacteristic
884C2×C3#550711yescharacteristic
885C2×C3C2×#89611yescharacteristic
886C2×C3D3×C22⋊Q811yescharacteristic
887C2×C3#562811yescharacteristic
888C2×C3#563111yescharacteristic
889C2×C3#563211yescharacteristic
890C2×C3D3×#12711yescharacteristic
891C2×C3#572411yescharacteristic
892C2×C3#572711yescharacteristic
893C2×C3#572711yescharacteristic
894C2×C3C2×#94011yescharacteristic
895C2×C3Q8×#6711yescharacteristic
896C2×C3#582411yescharacteristic
897D3—42no—
898D3—122no—
899D3—122no—
900D3—242no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—182no—
909C22—182no—
910C22—182no—
911C22—361no—
912C22—361no—
913C22—361no—
914C22—361no—
915C22#6429711yescharacteristic
916C22D3×#23511yescharacteristic
917C22D32×D411yescharacteristic
918C22D32×D411yescharacteristic
919C22#6431611yescharacteristic
920C22D32×Q811yescharacteristic
921C22C2×D3×#6711yescharacteristic
922C4—22no—
923C4—34no—
924C4—34no—
925C4—41no—
926C4—41no—
927C4—62no—
928C4—62no—
929C4—121no—
930C4—121no—
931C4—121no—
932C4—182no—
933C4—182no—
934C4—361no—
935C3—21no—
936C3#7433411yescharacteristic, complemented
937C3#8278011yescharacteristic, complemented
938C2—122no—
939C2—362no—
940C2#1059432811yescharacteristic
941C2#1059437811yescharacteristic
942C2#1059451611yescharacteristic
943C2D3×#89611yescharacteristic
944C2#1059488511yescharacteristic
945C2D3×#94011yescharacteristic
946C2#1059540311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#896C2semidirect
3. C2×#63895C2semidirect
4. C2×#63888C2semidirect
5. C2×#63851C2semidirect
6. C2×#63839C2semidirect
7. #10592692C2semidirect
8. C3×#4975C2semidirect
11. #10591324C2semidirect
12. #10591303C2semidirect
13. #10591244C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. #10591203C2semidirect
68. C2×#896D3semidirect
82. #4975D3semidirect
116. C2×#626Q8semidirect
134. C3×Dic3⋊C4D4semidirect
140. Dic3⋊Dic3D4semidirect
435. Dic3⋊C4#67semidirect
473. C3×Dic3C22⋊Q8semidirect
813. Dic3#896semidirect
815. C32#2542semidirect
936. C3#74334semidirect
937. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C2×#639042
C2×#638952
C2×#638882
C2×#638512
C2×#638392
#105926922
C3×#49752
#105913842
#105913832
#105913242
#105913032
#105912442
Dic3×Dic3⋊C42
#105912032
#827803
#743343