Finite Group Databasebeta

← C3×#80232 #11864680

Subgroups — C3×#80232 #11864680

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#918C211yesmaximal, characteristic, complemented
3C2×C3×#916C211yesmaximal, characteristic, complemented
4C3×#5629C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5173C211yesmaximal, characteristic, complemented
9C3×#5050C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4781C211yesmaximal, characteristic, complemented
13C3×#4771C211yesmaximal, characteristic, complemented
14C3×#4738C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3013—31nomaximal
17#80232C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C3×#1010—24no—
20C3×#1010—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×#237—21no—
25C2×C3×#237—21no—
26C2×C3×#237C2211yescharacteristic
27C2×C3×#237C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C22×C3×Dic6—21no—
31C22×C3×Dic6C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic
33C2×C32×SD16C2211yescharacteristic
34C32×C22⋊Q8C2211yescharacteristic
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic
37C2×C3×#216C2211yescharacteristic
38C2×C3×#215C2211yescharacteristic
39C2×C3×#213C2211yescharacteristic
40C3×#930C2211yescharacteristic
41C3×#918—24no—
42C3×#916—24no—
43C2×C3×#204C2211yescharacteristic
44C2×C3×#204C2211yescharacteristic
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
46C2×C3×D3×C8C2211yescharacteristic
47C3×#896—21no—
48C3×#895—21no—
49C3×#895C2211yescharacteristic
50C3×D3×C4⋊C4C2211yescharacteristic
51C3×#884—21no—
52C3×#884—21no—
53C32×#103C2211yescharacteristic
54C32×#102C2211yescharacteristic
55C32×C22⋊C8C2211yescharacteristic
56C3×#835C2211yescharacteristic
57C3×#832C2211yescharacteristic
58C3×#830C2211yescharacteristic
59C3×(C2×D3)⋊C8C2211yescharacteristic
60C3×(C2×D3)⋊C8C2211yescharacteristic
61C3×#816C2211yescharacteristic
62C3×#816C2211yescharacteristic
63C3×#810C2211yescharacteristic
64C3×#810C2211yescharacteristic
65C2×C3×2−1+4—31no—
66C2×#1010C2×C311yescharacteristic, complemented
67C2×C3×#137—31no—
68C2×C3×#135—31no—
69C3×#537—31no—
70C2×#918C2×C311yescharacteristic, complemented
71C2×#916C2×C311yescharacteristic, complemented
72#5629C2×C311yescharacteristic, complemented
73C3×#452—21no—
74C3×#452—31no—
75C3×#452D311yescharacteristic, complemented
76C3×#452C2×C311yescharacteristic, complemented
77C3×#451—31no—
78C3×#451—31no—
79C3×#449—31no—
80C3×#449—31no—
81C3×#448—31no—
82C3×#448—31no—
83C3×#417—31no—
84C2×C3×#103—31no—
85C3×#408—31no—
86#5238C2×C311yescharacteristic, complemented
87#5186C2×C311yescharacteristic, complemented
88#5173C2×C311yescharacteristic, complemented
89#5050C2×C311yescharacteristic, complemented
90#4806C2×C311yescharacteristic, complemented
91D3×#103C2×C311yescharacteristic, complemented
92#4781C2×C311yescharacteristic, complemented
93#4771C2×C311yescharacteristic, complemented
94#4738C2×C311yescharacteristic, complemented
95#4727C2×C311yescharacteristic, complemented
96C32×#41—22no—
97C32×#41—22no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—21no—
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67D411yescharacteristic
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C3×#239—22no—
113C3×#239—22no—
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C3×D3×Q8D414yescomplemented
118C3×#237—28no—
119C3×#237—28no—
120C3×#237—22no—
121C3×#237—22no—
122C3×#237—22no—
123C3×#237D414yescomplemented
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C2×C3×D12—21no—
128C2×C3×D12—21no—
129C2×C3×D12D411yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6—28no—
138C2×C3×Dic6—21no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6—21no—
141C2×C3×Dic6—22no—
142C2×C3×Dic6—22no—
143C2×C3×Dic6D411yescharacteristic
144C2×C3×Dic6C2311yescharacteristic
145C2×C3×Dic6C2311yescharacteristic
146C32×Q16—22no—
147C32×SD16—22no—
148C2×C32×C8C2311yescharacteristic
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4—21no—
151C32×C4⋊C4C2311yescharacteristic
152C32×C22⋊C4—21no—
153C3×#216—22no—
154C3×#216—22no—
155C3×#215—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×(C2×D3)⋊C4—21no—
159C3×(C2×D3)⋊C4—21no—
160C3×C4⋊Dic3C2311yescharacteristic
161C3×Dic3⋊C4—21no—
162C3×Dic3⋊C4—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164C2×C3×C3⋊C8C2311yescharacteristic
165C3×#204—22no—
166C3×#204—22no—
167C3×ΓL(1,𝔽25)—22no—
168C3×D3×C8—22no—
169#3013—31noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—31no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C2×C3×#41—61no—
180C2×C3×#41C2×D311yescharacteristic
181C2×C3×#41C22×C311yescharacteristic
182C22×C3×Q8—31no—
183C22×C3×Q8—31no—
184C22×C3×Q8—31no—
185C22×C3×Q8—61no—
186#1010—24no—
187#1010—24no—
188C2×#239C22×C311yescharacteristic
189C2×D3×Q8C22×C311yescharacteristic
190C2×D3×Q8C22×C311yescharacteristic
191C2×#237—21no—
192C2×#237—21no—
193C2×#237C22×C311yescharacteristic
194C2×#237C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235C22×C311yescharacteristic
197C22×Dic6—21no—
198C22×Dic6C22×C311yescharacteristic
199C3×#137—64no—
200C3×#135—64no—
201C2×C3×Q16—21no—
202C2×C3×Q16—31no—
203C2×C3×Q16—31no—
204C2×C3×Q16C2×D311yescharacteristic
205C2×C3×Q16C22×C311yescharacteristic
206C2×C3×SD16—21no—
207C2×C3×SD16—31no—
208C2×C3×SD16—31no—
209C2×C3×SD16—31no—
210C2×C3×SD16C2×D311yescharacteristic
211C2×C3×SD16C22×C311yescharacteristic
212C2×C3×D8—31no—
213C2×C3×M16—31no—
214C22×C3×C8—31no—
215C3×C22⋊Q8—21no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—61no—
218C3×C22⋊Q8C2×D311yescharacteristic
219C3×C22⋊Q8C22×C311yescharacteristic
220C3×#121—31no—
221C3×#121—31no—
222C3×#121—61no—
223C3×#121—61no—
224C3×#121—61no—
225C2×C3×C4⋊C4—31no—
226#946C22×C311yescharacteristic
227C2×#216C22×C311yescharacteristic
228C2×#216C22×C311yescharacteristic
229C2×#215C22×C311yescharacteristic
230C2×#213C22×C311yescharacteristic
231#930C22×C311yescharacteristic
232#918—24no—
233#916—24no—
234C2×#204C22×C311yescharacteristic
235C2×#204C22×C311yescharacteristic
236C2×ΓL(1,𝔽25)C22×C311yescharacteristic
237C2×D3×C8C22×C311yescharacteristic
238#896—21no—
239#895—21no—
240#895C22×C311yescharacteristic
241D3×C4⋊C4C22×C311yescharacteristic
242#884—21no—
243#884—21no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103—31no—
249C3×#103—31no—
250C3×#103C2×D311yescharacteristic
251C3×#103C22×C311yescharacteristic
252C3×#102—21no—
253C3×#102—31no—
254C3×#102C2×D311yescharacteristic
255C3×#102C22×C311yescharacteristic
256C3×C22⋊C8—21no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8C2×D311yescharacteristic
261C3×C22⋊C8C22×C311yescharacteristic
262#835C22×C311yescharacteristic
263#832C22×C311yescharacteristic
264#830C22×C311yescharacteristic
265(C2×D3)⋊C8C22×C311yescharacteristic
266(C2×D3)⋊C8C22×C311yescharacteristic
267#816C22×C311yescharacteristic
268#816C22×C311yescharacteristic
269#810C22×C311yescharacteristic
270#810C22×C311yescharacteristic
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3C2×D411yescharacteristic
275C22×C3×D3C2×D411yescharacteristic
276C32×Q8—21no—
277C32×Q8—21no—
278C32×Q8—21no—
279C32×Q8C2×D412yes—
280C32×D4—24no—
281C32×D4—21no—
282C32×D4C2×D412yes—
283C2×C32×C4—24no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291C3×#67—24no—
292C3×#67—22no—
293C3×#67—24no—
294C3×#67—22no—
295C3×#67—81no—
296C2×C3×Dic3—24no—
297C2×C3×Dic3—24no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—22no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—42no—
308C3×D12—81no—
309C3×C4×D3—24no—
310C3×C4×D3—24no—
311C3×C4×D3—21no—
312C3×C4×D3—21no—
313C3×C4×D3—42no—
314C3×C4×D3—81no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
317C3×Dic6—24no—
318C3×Dic6—24no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321C3×Dic6—22no—
322C3×Dic6—24no—
323C3×Dic6C2×D412yes—
324C3×Dic6C2×D412yes—
325C32×C8—21no—
326C32×C8—21no—
327C3×C3⋊C8—21no—
328C3×C3⋊C8—21no—
329C2×2−1+4—31no—
330C2×#137—31no—
331C2×#135—31no—
332#537—31no—
333#452—31no—
334#452C3×D311yescharacteristic, complemented
335#451—31no—
336#451—31no—
337#449—31no—
338#449—31no—
339#448—31no—
340#448—31no—
341#417—31no—
342C2×#103—31no—
343#408—31no—
344C3×#41—22no—
345C3×#41—22no—
346C3×#41—22no—
347C3×#41—22no—
348C3×#41—34no—
349C3×#41—42no—
350C3×#41—42no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—68no—
354C3×#41—62no—
355C3×#41—62no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—68no—
359C3×#41—68no—
360C3×#41—62no—
361C2×C3×Q8—21no—
362C2×C3×Q8—21no—
363C2×C3×Q8—31no—
364C2×C3×Q8—34no—
365C2×C3×Q8—31no—
366C2×C3×Q8—31no—
367C2×C3×Q8—61no—
368C2×C3×Q8—61no—
369C2×C3×Q8—62no—
370C2×C3×Q8—62no—
371C2×C3×Q8—68no—
372C2×C3×Q8—62no—
373C2×C3×Q8—62no—
374C2×C3×Q8—62no—
375C2×C3×Q8—61no—
376C2×C3×Q8C22×D311yescharacteristic
377C2×C3×Q8C22×D311yescharacteristic
378C2×C3×Q8C23×C311yescharacteristic
379C2×C3×Q8C23×C311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—41no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C2×C3×D4C22×D311yescharacteristic
394C2×C3×D4C23×C311yescharacteristic
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—41no—
401C22×C3×C4—61no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—61no—
406C22×C3×C4—61no—
407C22×C3×C4—61no—
408C22×C3×C4C22×D311yescharacteristic
409C22×C3×C4C23×C311yescharacteristic
410C2×#67—21no—
411C2×#67—21no—
412C2×#67—21no—
413C2×#67C3×D411yescharacteristic
414C2×#67C3×D411yescharacteristic
415C22×Dic3—21no—
416C22×Dic3—21no—
417C22×Dic3—21no—
418#239—22no—
419#239—22no—
420D3×Q8—22no—
421D3×Q8—22no—
422D3×Q8—22no—
423D3×Q8C3×D414yescomplemented
424#237—28no—
425#237—28no—
426#237—22no—
427#237—22no—
428#237—22no—
429#237C3×D414yescomplemented
430#235—28no—
431#235—22no—
432#235—22no—
433C2×D12—21no—
434C2×D12—21no—
435C2×D12C3×D411yescharacteristic
436C2×D12C23×C311yescharacteristic
437C2×C4×D3—21no—
438C2×C4×D3—21no—
439C2×C4×D3—21no—
440C2×C4×D3—21no—
441C2×C4×D3C23×C311yescharacteristic
442C2×C4×D3C23×C311yescharacteristic
443C2×Dic6—28no—
444C2×Dic6—21no—
445C2×Dic6—21no—
446C2×Dic6—21no—
447C2×Dic6—22no—
448C2×Dic6—22no—
449C2×Dic6C3×D411yescharacteristic
450C2×Dic6C23×C311yescharacteristic
451C2×Dic6C23×C311yescharacteristic
452C3×Q16—22no—
453C3×Q16—22no—
454C3×Q16—42no—
455C3×Q16—62no—
456C3×Q16—62no—
457C3×SD16—22no—
458C3×SD16—22no—
459C3×SD16—42no—
460C3×SD16—62no—
461C3×SD16—62no—
462C3×SD16—62no—
463C3×D8—62no—
464C3×M16—62no—
465C2×C3×C8—21no—
466C2×C3×C8—21no—
467C2×C3×C8—31no—
468C2×C3×C8—31no—
469C2×C3×C8—62no—
470C2×C3×C8C22×D311yescharacteristic
471C2×C3×C8C22×D311yescharacteristic
472C2×C3×C8C23×C311yescharacteristic
473C2×C3×C8C23×C311yescharacteristic
474C3×C4⋊C4—21no—
475C3×C4⋊C4—21no—
476C3×C4⋊C4—21no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—41no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4—61no—
481C3×C4⋊C4C22×D311yescharacteristic
482C3×C4⋊C4C23×C311yescharacteristic
483C3×C22⋊C4—21no—
484C3×C22⋊C4—21no—
485C3×C22⋊C4—41no—
486C3×C22⋊C4—61no—
487C3×C22⋊C4—61no—
488C3×C22⋊C4—61no—
489#216—22no—
490#216—22no—
491#215—22no—
492#213—22no—
493(C2×D3)⋊C4—21no—
494(C2×D3)⋊C4—21no—
495(C2×D3)⋊C4—21no—
496C4⋊Dic3C23×C311yescharacteristic
497Dic3⋊C4—21no—
498Dic3⋊C4—21no—
499C2×C3⋊C8C23×C311yescharacteristic
500C2×C3⋊C8C23×C311yescharacteristic
501#204—22no—
502#204—22no—
503ΓL(1,𝔽25)—22no—
504D3×C8—22no—
505C22×C32—21no—
506C22×C32—22no—
507C22×C32—21no—
508C22×C32—21no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32C22×D411yescharacteristic
512C2×C3×D3—21no—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—41no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3#12012yes—
521C32×C4—21no—
522C32×C4—22no—
523C32×C4—41no—
524C32×C4—41no—
525C32×C4C22×D411yescharacteristic
526C32×C4C22×D411yescharacteristic
527C3×Dic3—21no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—41no—
531C3×Dic3#12012yes—
5322−1+4—64no—
5332−1+4—64no—
534C2×#41—31no—
535C2×#41—31no—
536C2×#41—31no—
537C2×#41—31no—
538C2×#41—61no—
539C2×#41—61no—
540C2×#41—61no—
541C2×#41C2×C3×D311yescharacteristic
542C22×Q8—31no—
543C22×Q8—31no—
544C22×Q8—31no—
545C22×Q8—61no—
546#137—64no—
547#135—64no—
548C2×Q16—31no—
549C2×Q16—31no—
550C2×Q16C2×C3×D311yescharacteristic
551C2×SD16—31no—
552C2×SD16—31no—
553C2×SD16—31no—
554C2×SD16C2×C3×D311yescharacteristic
555C2×D8—31no—
556C2×M16—31no—
557C22×C8—31no—
558C22⋊Q8—31no—
559C22⋊Q8—61no—
560C22⋊Q8C2×C3×D311yescharacteristic
561#121—31no—
562#121—31no—
563#121—61no—
564#121—61no—
565#121—61no—
566C2×C4⋊C4—31no—
567#103—31no—
568#103—31no—
569#103—31no—
570#103—31no—
571#103—31no—
572#103C2×C3×D311yescharacteristic
573#102—31no—
574#102C2×C3×D311yescharacteristic
575C22⋊C8—31no—
576C22⋊C8—31no—
577C22⋊C8—31no—
578C22⋊C8C2×C3×D311yescharacteristic
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—41no—
585C23×C3—61no—
586C23×C3D3×D411yescharacteristic
587C23×C3C2×C3×D411yescharacteristic
588C22×D3—21no—
589C22×D3C2×C3×D411yescharacteristic
590C22×D3C2×C3×D411yescharacteristic
591C3×Q8—21no—
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—21no—
596C3×Q8—21no—
597C3×Q8—22no—
598C3×Q8—32no—
599C3×Q8—32no—
600C3×Q8—41no—
601C3×Q8—41no—
602C3×Q8—41no—
603C3×Q8—62no—
604C3×Q8—64no—
605C3×Q8—64no—
606C3×Q8—64no—
607C3×Q8—61no—
608C3×Q8—61no—
609C3×Q8D3×D412yes—
610C3×Q8C2×C3×D412yes—
611C3×D4—24no—
612C3×D4—24no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—22no—
616C3×D4—41no—
617C3×D4—44no—
618C3×D4—62no—
619C3×D4—62no—
620C3×D4—62no—
621C3×D4—64no—
622C3×D4—64no—
623C3×D4—61no—
624C3×D4—61no—
625C3×D4—122no—
626C3×D4—241no—
627C3×D4—241no—
628C3×D4D3×D412yes—
629C3×D4C2×C3×D412yes—
630C2×C3×C4—24no—
631C2×C3×C4—24no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—32no—
646C2×C3×C4—32no—
647C2×C3×C4—31no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—41no—
651C2×C3×C4—44no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—64no—
655C2×C3×C4—64no—
656C2×C3×C4—64no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—122no—
665C2×C3×C4—241no—
666C2×C3×C4D3×D411yescharacteristic
667C2×C3×C4C2×C3×D411yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C24×C311yescharacteristic
670#67—24no—
671#67—22no—
672#67—24no—
673#67—22no—
674#67—81no—
675C2×Dic3—24no—
676C2×Dic3—24no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—24no—
680C2×Dic3—21no—
681C2×Dic3C2×C3×D411yescharacteristic
682C2×Dic3C2×C3×D411yescharacteristic
683D12—22no—
684D12—21no—
685D12—21no—
686D12—42no—
687D12—81no—
688C4×D3—24no—
689C4×D3—24no—
690C4×D3—21no—
691C4×D3—21no—
692C4×D3—42no—
693C4×D3—81no—
694C4×D3C2×C3×D412yes—
695C4×D3C2×C3×D412yes—
696Dic6—24no—
697Dic6—24no—
698Dic6—21no—
699Dic6—21no—
700Dic6—22no—
701Dic6—24no—
702Dic6C2×C3×D412yes—
703Dic6C2×C3×D412yes—
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—41no—
709C3×C8—41no—
710C3×C8—61no—
711C3×C8—61no—
712C3⋊C8—21no—
713C3⋊C8—21no—
714C2×C32—41no—
715C2×C32—42no—
716C2×C32C2×#12011yescharacteristic
717C2×C32#57711yescharacteristic
718C2×C32#57811yescharacteristic
719C3×D3—22no—
720C3×D3—41no—
721C3×D3—81no—
722#41—22no—
723#41—22no—
724#41—34no—
725#41—62no—
726#41—62no—
727#41—68no—
728#41—62no—
729#41—62no—
730#41—62no—
731#41—62no—
732#41—68no—
733#41—68no—
734#41—62no—
735C2×Q8—31no—
736C2×Q8—34no—
737C2×Q8—31no—
738C2×Q8—31no—
739C2×Q8—61no—
740C2×Q8—61no—
741C2×Q8—62no—
742C2×Q8—62no—
743C2×Q8—68no—
744C2×Q8—62no—
745C2×Q8—62no—
746C2×Q8—62no—
747C2×Q8—61no—
748C2×Q8C22×C3×D311yescharacteristic
749C2×Q8C22×C3×D311yescharacteristic
750C2×D4—21no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—31no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4C22×C3×D311yescharacteristic
761C22×C4—21no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4C22×C3×D311yescharacteristic
772Q16—22no—
773Q16—62no—
774Q16—62no—
775SD16—22no—
776SD16—62no—
777SD16—62no—
778SD16—62no—
779D8—62no—
780M16—62no—
781C2×C8—31no—
782C2×C8—31no—
783C2×C8—62no—
784C2×C8C22×C3×D311yescharacteristic
785C2×C8C22×C3×D311yescharacteristic
786C4⋊C4—21no—
787C4⋊C4—31no—
788C4⋊C4—61no—
789C4⋊C4—61no—
790C4⋊C4C22×C3×D311yescharacteristic
791C22⋊C4—21no—
792C22⋊C4—61no—
793C22⋊C4—61no—
794C22⋊C4—61no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—22no—
801C22×C3—21no—
802C22×C3—22no—
803C22×C3—21no—
804C22×C3—32no—
805C22×C3—42no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—61no—
816C22×C3—61no—
817C22×C3—61no—
818C22×C3—81no—
819C22×C3—81no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3C2×D3×D411yescharacteristic
824C22×C3C22×C3×D411yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—21no—
830C2×D3—41no—
831C2×D3—41no—
832C2×D3—41no—
833C2×D3C3×#12012yes—
834C3×C4—21no—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—22no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—32no—
841C3×C4—41no—
842C3×C4—42no—
843C3×C4—41no—
844C3×C4—41no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—61no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—81no—
851C3×C4—81no—
852C3×C4—121no—
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×C3×D411yescharacteristic
856C3×C4C22×C3×D411yescharacteristic
857Dic3—21no—
858Dic3—22no—
859Dic3—22no—
860Dic3—41no—
861Dic3C3×#12012yes—
862C32#301311yescharacteristic, complemented, Sylow
863C23—21no—
864C23—31no—
865C23—31no—
866C23—61no—
867C23C3×D3×D411yescharacteristic
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—32no—
872Q8—32no—
873Q8—62no—
874Q8—64no—
875Q8—64no—
876Q8—64no—
877Q8—61no—
878Q8—61no—
879Q8C3×D3×D412yes—
880D4—24no—
881D4—21no—
882D4—62no—
883D4—62no—
884D4—62no—
885D4—64no—
886D4—64no—
887D4—61no—
888D4—61no—
889D4—122no—
890D4—241no—
891D4—241no—
892D4C3×D3×D412yes—
893C2×C4—24no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—31no—
900C2×C4—32no—
901C2×C4—32no—
902C2×C4—31no—
903C2×C4—64no—
904C2×C4—64no—
905C2×C4—64no—
906C2×C4—64no—
907C2×C4—64no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—61no—
913C2×C4—122no—
914C2×C4—241no—
915C2×C4C3×D3×D411yescharacteristic
916C2×C4C23×C3×D311yescharacteristic
917C8—21no—
918C8—21no—
919C8—61no—
920C8—61no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—41no—
925C2×C3—42no—
926C2×C3—41no—
927C2×C3—42no—
928C2×C3—62no—
929C2×C3—81no—
930C2×C3—82no—
931C2×C3—121no—
932C2×C3—241no—
933C2×C3D3×#12011yescharacteristic
934C2×C3#577011yescharacteristic
935C2×C3#577911yescharacteristic
936C2×C3C2×C3×#12011yescharacteristic
937C2×C3C3×#57711yescharacteristic
938C2×C3C3×#57811yescharacteristic
939D3—22no—
940D3—41no—
941D3—81no—
942C22—21no—
943C22—21no—
944C22—21no—
945C22—22no—
946C22—32no—
947C22—41no—
948C22—41no—
949C22—61no—
950C22—61no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—121no—
955C22—121no—
956C22—121no—
957C22C2×C3×D3×D411yescharacteristic
958C4—21no—
959C4—22no—
960C4—32no—
961C4—41no—
962C4—41no—
963C4—61no—
964C4—62no—
965C4—62no—
966C4—121no—
967C4C2×C3×D3×D411yescharacteristic
968C4C2×C3×D3×D411yescharacteristic
969C3—21no—
970C3#8023211yescharacteristic, direct product factor
971C3C3×#301311yescharacteristic, complemented
972C2—41no—
973C2—42no—
974C2—62no—
975C2—121no—
976C2—241no—
977C2C3×D3×#12011yescharacteristic
978C2C3×#577011yescharacteristic
979C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
hypercenterC3×#452D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#452

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×#918C2semidirect
3. C2×C3×#916C2semidirect
4. C3×#5629C2semidirect
5. C32×#452C2semidirect
6. C3×#5238C2semidirect
7. C3×#5186C2semidirect
8. C3×#5173C2semidirect
9. C3×#5050C2semidirect
10. C3×#4806C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4781C2semidirect
13. C3×#4771C2semidirect
14. C3×#4738C2semidirect
15. C3×#4727C2semidirect
17. #80232C3direct (N × H)
66. C2×#1010C2×C3semidirect
70. C2×#918C2×C3semidirect
71. C2×#916C2×C3semidirect
72. #5629C2×C3semidirect
75. C3×#452D3semidirect
76. C3×#452C2×C3semidirect
86. #5238C2×C3semidirect
87. #5186C2×C3semidirect
88. #5173C2×C3semidirect
89. #5050C2×C3semidirect
90. #4806C2×C3semidirect
91. D3×#103C2×C3semidirect
92. #4781C2×C3semidirect
93. #4771C2×C3semidirect
94. #4738C2×C3semidirect
95. #4727C2×C3semidirect
117. C3×D3×Q8D4semidirect
123. C3×#237D4semidirect
334. #452C3×D3semidirect
423. D3×Q8C3×D4semidirect
429. #237C3×D4semidirect
862. C32#3013semidirect
970. C3#80232direct (N × H)
971. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×#9182
C2×C3×#9162
C3×#56292
C32×#4522
C3×#52382
C3×#51862
C3×#51732
C3×#50502
C3×#48062
C3×D3×#1032
C3×#47812
C3×#47712
C3×#47382
C3×#47272
C3×#30133
#802323