Finite Group Databasebeta

← C3×#83528 #11884521

Subgroups — C3×#83528 #11884521

Order 1152.

1102 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic, complemented
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4C3×#5552C211yesmaximal, characteristic, complemented
5C3×#5239C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5090C211yesmaximal, characteristic, complemented
8C3×#5086C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#5050C211yesmaximal, characteristic, complemented
11C3×#5049C211yesmaximal, characteristic, complemented
12C3×#5047C211yesmaximal, characteristic, complemented
13C3×#5018C211yesmaximal, characteristic, complemented
14C3×#5016C211yesmaximal, characteristic, complemented
15C3×#5011C211yesmaximal, characteristic, complemented
16C3×#3269—31nomaximal
17#83528C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C32×#123—21no—
24C32×#123—21no—
25C32×C22⋊Q8C2211yescharacteristic
26C32×C22⋊Q8C2211yescharacteristic
27C32×#121—21no—
28C32×C4×D4C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic
30C2×C32×C4⋊C4—21no—
31C3×#951—24no—
32C3×#950—24no—
33C2×C3×#216C2211yescharacteristic
34C2×C3×#216C2211yescharacteristic
35C2×C3×#216C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C2×C3×#215C2211yescharacteristic
38C2×C3×#215C2211yescharacteristic
39C3×#939—21no—
40C2×C3×#214C2211yescharacteristic
41C2×C3×#214C2211yescharacteristic
42C2×C3×#213C2211yescharacteristic
43C3×#930C2211yescharacteristic
44C3×#924C2211yescharacteristic
45C2×C3×#208C2211yescharacteristic
46C22×C3×C3⋊C8C2211yescharacteristic
47C3×#896—21no—
48C3×#885—21no—
49C3×#67⋊C4—21no—
50C3×#875C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52C3×#835C2211yescharacteristic
53C3×#835C2211yescharacteristic
54C3×#832C2211yescharacteristic
55C3×#830C2211yescharacteristic
56C3×#830C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×C4⋊(C3⋊C8)C2211yescharacteristic
62C3×#803C2211yescharacteristic
63C2×C3×#137—31no—
64C2×C3×#135—31no—
65C3×#548—31no—
66C3×#547—21no—
67C3×#547D311yescharacteristic, complemented
68C3×#547C2×C311yescharacteristic, complemented
69C2×#951C2×C311yescharacteristic, complemented
70C2×#950C2×C311yescharacteristic, complemented
71#5552C2×C311yescharacteristic, complemented
72C3×#497—31no—
73C3×#468—31no—
74C3×#467—31no—
75C3×#463—31no—
76C3×#462—31no—
77C3×#452—31no—
78C3×#452—31no—
79C3×#451—31no—
80C3×#449—31no—
81C3×#440—31no—
82C3×#435—31no—
83#5239C2×C311yescharacteristic, complemented
84#5238C2×C311yescharacteristic, complemented
85#5090C2×C311yescharacteristic, complemented
86#5086C2×C311yescharacteristic, complemented
87#5051C2×C311yescharacteristic, complemented
88#5050C2×C311yescharacteristic, complemented
89#5049C2×C311yescharacteristic, complemented
90#5047C2×C311yescharacteristic, complemented
91#5018C2×C311yescharacteristic, complemented
92#5016C2×C311yescharacteristic, complemented
93#5011C2×C311yescharacteristic, complemented
94C32×#41—22no—
95C32×#41—22no—
96C32×#41—41no—
97C32×#41—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—21no—
101C2×C32×D4—21no—
102C2×C32×D4D411yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4—21no—
106C22×C32×C4—21no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C22×C3×Dic3—21no—
112C3×#235—22no—
113C3×#235—41no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×Dic6—22no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—41no—
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×C4⋊C4—21no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C4⋊C4—21no—
125C32×C4⋊C4D411yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4D411yescharacteristic
131C32×C22⋊C4D411yescharacteristic
132C32×C42C2311yescharacteristic
133C3×#217—21no—
134C3×#216—22no—
135C3×#216—22no—
136C3×#216—22no—
137C3×#216—41no—
138C3×#215—22no—
139C3×#215—41no—
140C3×#214—22no—
141C3×#214D414yescomplemented
142C3×#213—22no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C3×Dic3⋊C4—21no—
148C3×Dic3⋊C4—21no—
149C3×C4×Dic3—21no—
150C3×#208—22no—
151C2×C3×C3⋊C8—22no—
152C2×C3×C3⋊C8C2311yescharacteristic
153C2×C3×C3⋊C8C2311yescharacteristic
154C2×C3×C3⋊C8C2311yescharacteristic
155C2×C3×C3⋊C8C2311yescharacteristic
156#3269—31noSylow
157C2×C3×#41—21no—
158C2×C3×#41—21no—
159C2×C3×#41—31no—
160C2×C3×#41C2×D311yescharacteristic
161C2×C3×#41C2×D311yescharacteristic
162C2×C3×#41C22×C311yescharacteristic
163C2×C3×#41C22×C311yescharacteristic
164C22×C3×Q8—31no—
165C2×#235C22×C311yescharacteristic
166C22×Dic6C22×C311yescharacteristic
167C3×#137—64no—
168C3×#135—64no—
169C2×C3×Q16—31no—
170C2×C3×Q16—31no—
171C2×C3×Q16—31no—
172C2×C3×Q16—31no—
173C2×C3×SD16—31no—
174C2×C3×SD16—31no—
175C2×C3×SD16—31no—
176C2×C3×SD16—31no—
177C2×C3×D8—31no—
178C2×C3×M16—31no—
179C22×C3×C8—31no—
180C3×C4⋊Q8—21no—
181C3×C4⋊Q8C2×D311yescharacteristic
182C3×C4⋊Q8C22×C311yescharacteristic
183C3×#124—31no—
184C3×#124—61no—
185C3×#123—22no—
186C3×#123—22no—
187C3×#123—21no—
188C3×#123—21no—
189C3×#123—21no—
190C3×#123—21no—
191C3×C22⋊Q8—21no—
192C3×C22⋊Q8—21no—
193C3×C22⋊Q8—31no—
194C3×C22⋊Q8—61no—
195C3×C22⋊Q8C2×D311yescharacteristic
196C3×C22⋊Q8C2×D311yescharacteristic
197C3×C22⋊Q8C22×C311yescharacteristic
198C3×C22⋊Q8C22×C311yescharacteristic
199C3×#121—22no—
200C3×#121—21no—
201C3×#121—21no—
202C3×#121—31no—
203C3×#121—61no—
204C3×C4×Q8—31no—
205C3×C4×D4—21no—
206C3×C4×D4—21no—
207C3×C4×D4—61no—
208C3×C4×D4C2×D311yescharacteristic
209C3×C4×D4C2×D311yescharacteristic
210C3×C4×D4C22×C311yescharacteristic
211C3×C4×D4C22×C311yescharacteristic
212C2×C3×C4⋊C4—22no—
213C2×C3×C4⋊C4—21no—
214C2×C3×C4⋊C4—21no—
215#951—24no—
216#950—24no—
217C2×#216C22×C311yescharacteristic
218C2×#216C22×C311yescharacteristic
219C2×#216C22×C311yescharacteristic
220C2×#216C22×C311yescharacteristic
221C2×#215C22×C311yescharacteristic
222C2×#215C22×C311yescharacteristic
223#939—21no—
224C2×#214C22×C311yescharacteristic
225C2×#214C22×C311yescharacteristic
226C2×#213C22×C311yescharacteristic
227#930C22×C311yescharacteristic
228#924C22×C311yescharacteristic
229C2×#208C22×C311yescharacteristic
230C22×C3⋊C8C22×C311yescharacteristic
231#896—21no—
232#885—21no—
233#67⋊C4—21no—
234#875C22×C311yescharacteristic
235C4×Dic6C22×C311yescharacteristic
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#103—31no—
241C3×#103—31no—
242C3×#102—31no—
243C3×#102—31no—
244C3×C22⋊C8—31no—
245C3×C22⋊C8—31no—
246C3×#97—31no—
247#835C22×C311yescharacteristic
248#835C22×C311yescharacteristic
249#832C22×C311yescharacteristic
250#830C22×C311yescharacteristic
251#830C22×C311yescharacteristic
252#810C22×C311yescharacteristic
253#810C22×C311yescharacteristic
254#809C22×C311yescharacteristic
255#807C22×C311yescharacteristic
256C4⋊(C3⋊C8)C22×C311yescharacteristic
257#803C22×C311yescharacteristic
258C23×C32—21no—
259C23×C32C2×D411yescharacteristic
260C23×C32C2×D411yescharacteristic
261C22×C3×D3—21no—
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C32×D4—21no—
267C32×D4—41no—
268C32×D4—42no—
269C32×D4—42no—
270C32×D4C2×D412yes—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—42no—
279C2×C32×C4—42no—
280C2×C32×C4—42no—
281C2×C32×C4C2×D411yescharacteristic
282C2×C32×C4C2×D411yescharacteristic
283C2×C32×C4C2×D411yescharacteristic
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2411yescharacteristic
286C3×#67—42no—
287C3×#67—42no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—42no—
292C3×D12—21no—
293C3×D12—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C3×Dic6C2×D412yes—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8C2×D412yes—
304C2×#137—31no—
305C2×#135—31no—
306#548—31no—
307#547C3×D311yescharacteristic, complemented
308#497—31no—
309#468—31no—
310#467—31no—
311#463—31no—
312#462—31no—
313#452—31no—
314#452—31no—
315#451—31no—
316#449—31no—
317#440—31no—
318#435—31no—
319C3×#41—22no—
320C3×#41—22no—
321C3×#41—22no—
322C3×#41—22no—
323C3×#41—42no—
324C3×#41—42no—
325C3×#41—41no—
326C3×#41—41no—
327C3×#41—41no—
328C3×#41—41no—
329C3×#41—42no—
330C3×#41—42no—
331C3×#41—62no—
332C3×#41—121no—
333C2×C3×Q8—21no—
334C2×C3×Q8—21no—
335C2×C3×Q8—31no—
336C2×C3×Q8—31no—
337C2×C3×Q8—62no—
338C2×C3×Q8—61no—
339C2×C3×Q8—121no—
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×Q8C22×D311yescharacteristic
342C2×C3×Q8C23×C311yescharacteristic
343C2×C3×Q8C23×C311yescharacteristic
344C2×C3×D4—22no—
345C2×C3×D4—22no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—31no—
353C2×C3×D4—61no—
354C2×C3×D4—61no—
355C2×C3×D4#6711yescharacteristic
356C2×C3×D4C3×D411yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C2×C3×D4C23×C311yescharacteristic
359C22×C3×C4—22no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—61no—
371C22×C3×C4—61no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C23×C311yescharacteristic
375C22×C3×C4C23×C311yescharacteristic
376C2×#67—21no—
377C2×#67—21no—
378C22×Dic3—21no—
379#235—22no—
380#235—41no—
381C2×D12C23×C311yescharacteristic
382C2×C4×D3—21no—
383C2×Dic6—22no—
384C2×Dic6—21no—
385C2×Dic6—41no—
386C2×Dic6C23×C311yescharacteristic
387C2×Dic6C23×C311yescharacteristic
388C3×Q16—62no—
389C3×Q16—62no—
390C3×Q16—62no—
391C3×Q16—121no—
392C3×SD16—34no—
393C3×SD16—62no—
394C3×SD16—62no—
395C3×SD16—121no—
396C3×D8—62no—
397C3×M16—62no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8—31no—
401C2×C3×C8—31no—
402C2×C3×C8—62no—
403C3×C4⋊C4—22no—
404C3×C4⋊C4—22no—
405C3×C4⋊C4—22no—
406C3×C4⋊C4—22no—
407C3×C4⋊C4—21no—
408C3×C4⋊C4—21no—
409C3×C4⋊C4—21no—
410C3×C4⋊C4—21no—
411C3×C4⋊C4—21no—
412C3×C4⋊C4—21no—
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—21no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—61no—
419C3×C4⋊C4—61no—
420C3×C4⋊C4#6711yescharacteristic
421C3×C4⋊C4C3×D411yescharacteristic
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C23×C311yescharacteristic
424C3×C22⋊C4—22no—
425C3×C22⋊C4—22no—
426C3×C22⋊C4—22no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—21no—
429C3×C22⋊C4—21no—
430C3×C22⋊C4—21no—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4—21no—
434C3×C22⋊C4—21no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—61no—
437C3×C22⋊C4—61no—
438C3×C22⋊C4—61no—
439C3×C22⋊C4#6711yescharacteristic
440C3×C22⋊C4#6711yescharacteristic
441C3×C22⋊C4C3×D411yescharacteristic
442C3×C22⋊C4C3×D411yescharacteristic
443C3×C42—21no—
444C3×C42—61no—
445C3×C42C22×D311yescharacteristic
446C3×C42C23×C311yescharacteristic
447#217—21no—
448#216—22no—
449#216—22no—
450#216—22no—
451#216—41no—
452#215—22no—
453#215—41no—
454#214—22no—
455#214C3×D414yescomplemented
456#213—22no—
457(C2×D3)⋊C4—21no—
458(C2×D3)⋊C4—21no—
459(C2×D3)⋊C4—21no—
460C4⋊Dic3C23×C311yescharacteristic
461Dic3⋊C4—21no—
462Dic3⋊C4—21no—
463C4×Dic3—21no—
464#208—22no—
465C2×C3⋊C8—22no—
466C2×C3⋊C8C23×C311yescharacteristic
467C2×C3⋊C8C23×C311yescharacteristic
468C2×C3⋊C8C23×C311yescharacteristic
469C2×C3⋊C8C23×C311yescharacteristic
470C22×C32—22no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—21no—
487C32×C4—41no—
488C32×C4—41no—
489C32×C4—41no—
490C32×C4C22×D411yescharacteristic
491C32×C4H(5,𝔽2)11yescharacteristic
492C3×Dic3—22no—
493C3×Dic3—41no—
494C3×Dic3—41no—
495C2×#41—31no—
496C2×#41C2×C3×D311yescharacteristic
497C2×#41C2×C3×D311yescharacteristic
498C22×Q8—31no—
499#137—64no—
500#135—64no—
501C2×Q16—31no—
502C2×Q16—31no—
503C2×Q16—31no—
504C2×Q16—31no—
505C2×SD16—31no—
506C2×SD16—31no—
507C2×SD16—31no—
508C2×SD16—31no—
509C2×D8—31no—
510C2×M16—31no—
511C22×C8—31no—
512C4⋊Q8C2×C3×D311yescharacteristic
513#124—31no—
514#124—61no—
515#123—21no—
516#123—21no—
517C22⋊Q8—31no—
518C22⋊Q8—61no—
519C22⋊Q8C2×C3×D311yescharacteristic
520C22⋊Q8C2×C3×D311yescharacteristic
521#121—21no—
522#121—31no—
523#121—61no—
524C4×Q8—31no—
525C4×D4—61no—
526C4×D4C2×C3×D311yescharacteristic
527C4×D4C2×C3×D311yescharacteristic
528C2×C4⋊C4—21no—
529#107—31no—
530C4⋊C8—31no—
531#103—31no—
532#103—31no—
533#103—31no—
534#103—31no—
535#102—31no—
536#102—31no—
537C22⋊C8—31no—
538C22⋊C8—31no—
539#97—31no—
540C23×C3—22no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—61no—
546C23×C3C2×#6711yescharacteristic
547C23×C3C2×#6711yescharacteristic
548C23×C3C2×C3×D411yescharacteristic
549C23×C3C2×C3×D411yescharacteristic
550C22×D3—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—32no—
560C3×Q8—41no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—41no—
564C3×Q8—61no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×Q8—122no—
568C3×D4—22no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—22no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—42no—
577C3×D4—42no—
578C3×D4—42no—
579C3×D4—44no—
580C3×D4—44no—
581C3×D4—61no—
582C3×D4—61no—
583C3×D4—122no—
584C3×D4—122no—
585C3×D4D3×D412yes—
586C3×D4C2×C3×D412yes—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—44no—
618C2×C3×C4—42no—
619C2×C3×C4—42no—
620C2×C3×C4—44no—
621C2×C3×C4—44no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—122no—
626C2×C3×C4—122no—
627C2×C3×C4C2×#6711yescharacteristic
628C2×C3×C4C2×#6711yescharacteristic
629C2×C3×C4C2×#6711yescharacteristic
630C2×C3×C4C2×#6711yescharacteristic
631C2×C3×C4C2×C3×D411yescharacteristic
632C2×C3×C4C2×C3×D411yescharacteristic
633C2×C3×C4C2×C3×D411yescharacteristic
634C2×C3×C4C2×C3×D411yescharacteristic
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C24×C311yescharacteristic
637#67—42no—
638#67—42no—
639C2×Dic3—21no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—42no—
643D12—21no—
644D12—21no—
645C4×D3—42no—
646Dic6—21no—
647Dic6—21no—
648Dic6—21no—
649Dic6—42no—
650Dic6C2×C3×D412yes—
651C3×C8—32no—
652C3×C8—61no—
653C3×C8—61no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C3⋊C8—21no—
658C3⋊C8C2×C3×D412yes—
659C2×C32—42no—
660C2×C32—41no—
661C2×C32—41no—
662C2×C32D4211yescharacteristic
663C2×C32#57511yescharacteristic
664C2×C32#57811yescharacteristic
665C3×D3—81no—
666#41—22no—
667#41—22no—
668#41—41no—
669#41—41no—
670#41—62no—
671#41—121no—
672C2×Q8—31no—
673C2×Q8—31no—
674C2×Q8—62no—
675C2×Q8—61no—
676C2×Q8—121no—
677C2×Q8C22×C3×D311yescharacteristic
678C2×Q8C22×C3×D311yescharacteristic
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—31no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4C3×#6711yescharacteristic
685C2×D4C22×C3×D311yescharacteristic
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D311yescharacteristic
693Q16—62no—
694Q16—62no—
695Q16—62no—
696Q16—121no—
697SD16—34no—
698SD16—62no—
699SD16—62no—
700SD16—121no—
701D8—62no—
702M16—62no—
703C2×C8—31no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—31no—
713C4⋊C4—61no—
714C4⋊C4—61no—
715C4⋊C4C3×#6711yescharacteristic
716C4⋊C4C22×C3×D311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—61no—
721C22⋊C4—61no—
722C22⋊C4—61no—
723C22⋊C4—61no—
724C22⋊C4C3×#6711yescharacteristic
725C22⋊C4C3×#6711yescharacteristic
726C42—61no—
727C42C22×C3×D311yescharacteristic
728C22×C3—24no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3C22×#6711yescharacteristic
760C22×C3C22×C3×D411yescharacteristic
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C3×C4—22no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—41no—
778C3×C4—42no—
779C3×C4—42no—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—41no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—62no—
788C3×C4—121no—
789C3×C4—121no—
790C3×C4C2×D3×D411yescharacteristic
791C3×C4#100411yescharacteristic
792C3×C4C22×C3×D411yescharacteristic
793C3×C4C3×H(5,𝔽2)11yescharacteristic
794Dic3—22no—
795Dic3—41no—
796Dic3—41no—
797C32#326911yescharacteristic, complemented, Sylow
798C23—21no—
799C23—61no—
800C23C2×C3×#6711yescharacteristic
801C23C2×C3×#6711yescharacteristic
802Q8—21no—
803Q8—21no—
804Q8—21no—
805Q8—21no—
806Q8—32no—
807Q8—61no—
808Q8—61no—
809Q8—61no—
810Q8—122no—
811D4—21no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—61no—
816D4—61no—
817D4—122no—
818D4—122no—
819D4C3×D3×D412yes—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—61no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4C2×C3×#6711yescharacteristic
836C2×C4C2×C3×#6711yescharacteristic
837C2×C4C2×C3×#6711yescharacteristic
838C2×C4C2×C3×#6711yescharacteristic
839C2×C4C23×C3×D311yescharacteristic
840C8—32no—
841C8—61no—
842C8—61no—
843C8—61no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—44no—
848C2×C3—41no—
849C2×C3—41no—
850C2×C3—42no—
851C2×C3—41no—
852C2×C3—41no—
853C2×C3—42no—
854C2×C3—81no—
855C2×C3—81no—
856C2×C3—241no—
857C2×C3D4×#6711yescharacteristic
858C2×C3#582211yescharacteristic
859C2×C3#583811yescharacteristic
860C2×C3C3×D4211yescharacteristic
861C2×C3C3×#57511yescharacteristic
862C2×C3C3×#57811yescharacteristic
863D3—81no—
864C22—21no—
865C22—21no—
866C22—22no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22C22×C3×#6711yescharacteristic
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—62no—
885C4—121no—
886C4—121no—
887C4C2×C3×D3×D411yescharacteristic
888C4C3×#100411yescharacteristic
889C3—21no—
890C3#8352811yescharacteristic, direct product factor
891C3C3×#326911yescharacteristic, complemented
892C2—41no—
893C2—41no—
894C2—42no—
895C2—241no—
896C2C3×D4×#6711yescharacteristic
897C2C3×#582211yescharacteristic
898C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#547C2
socleC22×C32C22×D4
hypercenterC3×#547D3
hypocenterC3C3×#3269
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
1. C32×#547C2semidirect
2. C2×C3×#951C2semidirect
3. C2×C3×#950C2semidirect
4. C3×#5552C2semidirect
5. C3×#5239C2semidirect
6. C3×#5238C2semidirect
7. C3×#5090C2semidirect
8. C3×#5086C2semidirect
9. C3×#5051C2semidirect
10. C3×#5050C2semidirect
11. C3×#5049C2semidirect
12. C3×#5047C2semidirect
13. C3×#5018C2semidirect
14. C3×#5016C2semidirect
15. C3×#5011C2semidirect
17. #83528C3direct (N × H)
67. C3×#547D3semidirect
68. C3×#547C2×C3semidirect
69. C2×#951C2×C3semidirect
70. C2×#950C2×C3semidirect
71. #5552C2×C3semidirect
83. #5239C2×C3semidirect
84. #5238C2×C3semidirect
85. #5090C2×C3semidirect
86. #5086C2×C3semidirect
87. #5051C2×C3semidirect
88. #5050C2×C3semidirect
89. #5049C2×C3semidirect
90. #5047C2×C3semidirect
91. #5018C2×C3semidirect
92. #5016C2×C3semidirect
93. #5011C2×C3semidirect
141. C3×#214D4semidirect
307. #547C3×D3semidirect
455. #214C3×D4semidirect
797. C32#3269semidirect
890. C3#83528direct (N × H)
891. C3C3×#3269semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
C2×C3×#9512
C2×C3×#9502
C3×#55522
C3×#52392
C3×#52382
C3×#50902
C3×#50862
C3×#50512
C3×#50502
C3×#50492
C3×#50472
C3×#50182
C3×#50162
C3×#50112
C3×#32693
#835283