Finite Group Databasebeta

← C3×#80084 #11864108

Subgroups — C3×#80084 #11864108

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#914C211yesmaximal, characteristic, complemented
3C2×C3×#911C211yesmaximal, characteristic, complemented
4C3×D3×#121C211yesmaximal, characteristic, complemented
5C32×#449C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7C3×#5170C211yesmaximal, characteristic, complemented
8C3×#5156C211yesmaximal, characteristic, complemented
9C3×#5037C211yesmaximal, characteristic, complemented
10C3×#4806C211yesmaximal, characteristic, complemented
11C3×#4803C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×#4771C211yesmaximal, characteristic, complemented
14C3×#4734C211yesmaximal, characteristic, complemented
15C3×#4726C211yesmaximal, characteristic, complemented
16C3×#3006—31nomaximal
17#80084C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4—21no—
27C2×C3×D3×D4C2211yescharacteristic, complemented
28C2×C3×D3×D4C2211yescharacteristic, complemented
29C2×C3×#235—21no—
30C2×C3×#235C2211yescharacteristic, complemented
31C22×C3×C4×D3—21no—
32C22×C3×C4×D3C2211yescharacteristic
33C2×C32×SD16C2211yescharacteristic, complemented
34C2×C32×D8C2211yescharacteristic, complemented
35C32×#121C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C3×#939—21no—
38C3×#938C2211yescharacteristic
39C2×C3×#214C2211yescharacteristic, complemented
40C2×C3×#213C2211yescharacteristic, complemented
41C2×C3×#213C2211yescharacteristic, complemented
42C3×#930C2211yescharacteristic, complemented
43C3×#914—24no—
44C3×#911—24no—
45C2×C3×D24C2211yescharacteristic, complemented
46C2×C3×#204C2211yescharacteristic, complemented
47C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
48C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
49C3×#895C2211yescharacteristic
50C3×D3×C4⋊C4C2211yescharacteristic, complemented
51C3×#884—21no—
52C3×D3×C22⋊C4—21no—
53C32×#103C2211yescharacteristic, complemented
54C32×#102C2211yescharacteristic, complemented
55C32×C22⋊C8C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59C3×#821C2211yescharacteristic, complemented
60C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
61C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
62C3×#816C2211yescharacteristic, complemented
63C3×#810C2211yescharacteristic, complemented
64C3×#809C2211yescharacteristic, complemented
65C22×C3×#41—31no—
66C2×D3×#41C2×C311yescharacteristic, complemented
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×C3×AGL(1,ℤ/8)—31no—
69C2×C3×#121—31no—
70C2×#914C2×C311yescharacteristic, complemented
71C2×#911C2×C311yescharacteristic, complemented
72D3×#121C2×C311yescharacteristic, complemented
73C3×#449—21no—
74C3×#449—31no—
75C3×#449—31no—
76C3×#449—31no—
77C3×#449D311yescharacteristic, complemented
78C3×#449C2×C311yescharacteristic, complemented
79C3×#448—31no—
80C3×#448—31no—
81C3×#447—31no—
82C3×#447—31no—
83C3×#417—31no—
84C3×#417—31no—
85C3×#407—31no—
86#5238C2×C311yescharacteristic, complemented
87#5170C2×C311yescharacteristic, complemented
88#5156C2×C311yescharacteristic, complemented
89#5037C2×C311yescharacteristic, complemented
90#4806C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92#4773C2×C311yescharacteristic, complemented
93#4771C2×C311yescharacteristic, complemented
94#4734C2×C311yescharacteristic, complemented
95#4726C2×C311yescharacteristic, complemented
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3D411yescharacteristic
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4—21no—
104C2×C32×D4C2311yescharacteristic
105C2×C32×D4C2311yescharacteristic
106C22×C32×C4—21no—
107C22×C32×C4C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C22×C3×Dic3—21no—
115C22×C3×Dic3D411yescharacteristic
116C3×#239—22no—
117C3×#239D414yescomplemented
118C3×D3×Q8—22no—
119C3×D3×Q8—22no—
120C3×#237—28no—
121C3×#237—22no—
122C3×#237D414yescomplemented
123C3×D3×D4—28no—
124C3×D3×D4—22no—
125C3×D3×D4—22no—
126C3×D3×D4—22no—
127C3×D3×D4—22no—
128C3×D3×D4—44no—
129C3×#235—28no—
130C3×#235—22no—
131C3×#235—22no—
132C2×C3×D12—21no—
133C2×C3×D12—21no—
134C2×C3×D12C2311yescharacteristic
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3—28no—
137C2×C3×C4×D3—21no—
138C2×C3×C4×D3—21no—
139C2×C3×C4×D3—21no—
140C2×C3×C4×D3—22no—
141C2×C3×C4×D3—22no—
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3D411yescharacteristic
144C2×C3×C4×D3D411yescharacteristic
145C2×C3×C4×D3C2311yescharacteristic
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×Dic6—21no—
148C2×C3×Dic6C2311yescharacteristic
149C32×SD16—22no—
150C32×D8—22no—
151C2×C32×C8C2311yescharacteristic
152C2×C32×C8C2311yescharacteristic
153C32×C4⋊C4C2311yescharacteristic
154C32×C22⋊C4—21no—
155C3×#217—21no—
156C3×#215—22no—
157C3×#214—22no—
158C3×#213—22no—
159C3×#213—22no—
160C3×(C2×D3)⋊C4—21no—
161C3×(C2×D3)⋊C4—21no—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4—21no—
164C2×C3×C3⋊C8C2311yescharacteristic
165C2×C3×C3⋊C8C2311yescharacteristic
166C3×D24—22no—
167C3×#204—22no—
168C3×ΓL(1,𝔽25)—22no—
169C3×ΓL(1,𝔽25)—22no—
170#3006—31noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—61no—
176C2×C3×#41—61no—
177C2×C3×#41—64no—
178C2×C3×#41—64no—
179C2×C3×#41C2×D311yescharacteristic, complemented
180C2×C3×#41C22×C311yescharacteristic, complemented
181C22×C3×Q8—31no—
182C22×C3×D4—31no—
183C22×C3×D4—31no—
184C22×C3×D4—61no—
185C22×C3×D4—61no—
186C23×C3×C4—31no—
187C23×C3×C4—61no—
188D3×#41—24no—
189D3×#41—24no—
190C2×#239C22×C311yescharacteristic
191C2×D3×Q8C22×C311yescharacteristic, complemented
192C2×#237—21no—
193C2×#237C22×C311yescharacteristic
194C2×D3×D4—21no—
195C2×D3×D4—21no—
196C2×D3×D4C22×C311yescharacteristic, complemented
197C2×D3×D4C22×C311yescharacteristic, complemented
198C2×#235—21no—
199C2×#235C22×C311yescharacteristic, complemented
200C22×C4×D3—21no—
201C22×C4×D3C22×C311yescharacteristic
202C3×AGL(1,ℤ/8)—64no—
203C3×AGL(1,ℤ/8)—64no—
204C2×C3×SD16—21no—
205C2×C3×SD16—31no—
206C2×C3×SD16—31no—
207C2×C3×SD16—31no—
208C2×C3×SD16C2×D311yescharacteristic, complemented
209C2×C3×SD16C22×C311yescharacteristic, complemented
210C2×C3×D8—21no—
211C2×C3×D8—31no—
212C2×C3×D8—31no—
213C2×C3×D8—31no—
214C2×C3×D8C2×D311yescharacteristic, complemented
215C2×C3×D8C22×C311yescharacteristic, complemented
216C2×C3×M16—31no—
217C2×C3×M16—31no—
218C3×#121—21no—
219C3×#121—31no—
220C3×#121—31no—
221C3×#121—31no—
222C3×#121—61no—
223C3×#121—61no—
224C3×#121C2×D311yescharacteristic, complemented
225C3×#121C22×C311yescharacteristic, complemented
226C2×C3×C4⋊C4—31no—
227C2×C3×C22⋊C4—61no—
228C2×#215C22×C311yescharacteristic, complemented
229#939—21no—
230#938C22×C311yescharacteristic
231C2×#214C22×C311yescharacteristic, complemented
232C2×#213C22×C311yescharacteristic, complemented
233C2×#213C22×C311yescharacteristic, complemented
234#930C22×C311yescharacteristic, complemented
235#914—24no—
236#911—24no—
237C2×D24C22×C311yescharacteristic, complemented
238C2×#204C22×C311yescharacteristic, complemented
239C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
240C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
241#895C22×C311yescharacteristic
242D3×C4⋊C4C22×C311yescharacteristic, complemented
243#884—21no—
244D3×C22⋊C4—21no—
245C3×#103—21no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103—31no—
249C3×#103C2×D311yescharacteristic, complemented
250C3×#103C22×C311yescharacteristic, complemented
251C3×#102—21no—
252C3×#102—31no—
253C3×#102—31no—
254C3×#102—31no—
255C3×#102C2×D311yescharacteristic, complemented
256C3×#102C22×C311yescharacteristic, complemented
257C3×C22⋊C8—21no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8—31no—
261C3×C22⋊C8C2×D311yescharacteristic, complemented
262C3×C22⋊C8C22×C311yescharacteristic, complemented
263#835C22×C311yescharacteristic, complemented
264#832C22×C311yescharacteristic, complemented
265#830C22×C311yescharacteristic, complemented
266#821C22×C311yescharacteristic, complemented
267(C2×D3)⋊C8C22×C311yescharacteristic, complemented
268(C2×D3)⋊C8C22×C311yescharacteristic, complemented
269#816C22×C311yescharacteristic, complemented
270#810C22×C311yescharacteristic, complemented
271#809C22×C311yescharacteristic, complemented
272C23×C32—21no—
273C23×C32—21no—
274C23×C32C2×D411yescharacteristic
275C22×C3×D3—24no—
276C22×C3×D3—21no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—21no—
280C22×C3×D3—41no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3—42no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3C2×D411yescharacteristic
287C22×C3×D3C2×D411yescharacteristic
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C32×D4—24no—
291C32×D4—21no—
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—42no—
295C32×D4C2×D412yescomplemented
296C2×C32×C4—24no—
297C2×C32×C4—21no—
298C2×C32×C4—21no—
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4C2×D411yescharacteristic
302C2×C32×C4C2411yescharacteristic
303C3×#67—24no—
304C3×#67—24no—
305C3×#67—24no—
306C3×#67—42no—
307C3×#67—42no—
308C3×#67—42no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—24no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3C2×D411yescharacteristic
314C2×C3×Dic3C2×D411yescharacteristic
315C3×D12—24no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12—21no—
319C3×D12—42no—
320C3×D12C2×D412yescomplemented
321C3×C4×D3—24no—
322C3×C4×D3—24no—
323C3×C4×D3—22no—
324C3×C4×D3—21no—
325C3×C4×D3—21no—
326C3×C4×D3—22no—
327C3×C4×D3—24no—
328C3×C4×D3—42no—
329C3×C4×D3C2×D412yes—
330C3×C4×D3C2×D412yes—
331C3×Dic6—24no—
332C3×Dic6—21no—
333C3×Dic6C2×D412yescomplemented
334C32×C8—21no—
335C32×C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—31no—
339C2×AGL(1,ℤ/8)—31no—
340C2×AGL(1,ℤ/8)—31no—
341C2×#121—31no—
342#449—31no—
343#449—31no—
344#449—31no—
345#449C3×D311yescharacteristic, complemented
346#448—31no—
347#448—31no—
348#447—31no—
349#447—31no—
350#417—31no—
351#417—31no—
352#407—31no—
353C24×C3—31no—
354C24×C3—61no—
355C24×C3—61no—
356C23×D3—21no—
357C23×D3—21no—
358C23×D3C3×D411yescharacteristic
359C3×#41—22no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—34no—
364C3×#41—34no—
365C3×#41—42no—
366C3×#41—42no—
367C3×#41—62no—
368C3×#41—62no—
369C3×#41—68no—
370C3×#41—62no—
371C3×#41—62no—
372C3×#41—68no—
373C2×C3×Q8—21no—
374C2×C3×Q8—31no—
375C2×C3×Q8—61no—
376C2×C3×Q8—62no—
377C2×C3×Q8—62no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C23×C311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—21no—
384C2×C3×D4—21no—
385C2×C3×D4—21no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—41no—
389C2×C3×D4—41no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—62no—
394C2×C3×D4—61no—
395C2×C3×D4—61no—
396C2×C3×D4—62no—
397C2×C3×D4—68no—
398C2×C3×D4—61no—
399C2×C3×D4—61no—
400C2×C3×D4—62no—
401C2×C3×D4—61no—
402C2×C3×D4—61no—
403C2×C3×D4—124no—
404C2×C3×D4C22×D311yescharacteristic
405C2×C3×D4C22×D311yescharacteristic
406C2×C3×D4C23×C311yescharacteristic
407C2×C3×D4C23×C311yescharacteristic
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—41no—
417C22×C3×C4—62no—
418C22×C3×C4—62no—
419C22×C3×C4—61no—
420C22×C3×C4—61no—
421C22×C3×C4—68no—
422C22×C3×C4—61no—
423C22×C3×C4—61no—
424C22×C3×C4—61no—
425C22×C3×C4C22×D311yescharacteristic
426C22×C3×C4C23×C311yescharacteristic
427C2×#67—21no—
428C2×#67—21no—
429C2×#67—21no—
430C2×#67—21no—
431C2×#67—21no—
432C2×#67—21no—
433C22×Dic3—21no—
434C22×Dic3C3×D411yescharacteristic
435#239—22no—
436#239C3×D414yescomplemented
437D3×Q8—22no—
438D3×Q8—22no—
439#237—28no—
440#237—22no—
441#237C3×D414yescomplemented
442D3×D4—28no—
443D3×D4—22no—
444D3×D4—22no—
445D3×D4—22no—
446D3×D4—22no—
447D3×D4—44no—
448#235—28no—
449#235—22no—
450#235—22no—
451C2×D12—21no—
452C2×D12—21no—
453C2×D12C23×C311yescharacteristic
454C2×D12C23×C311yescharacteristic
455C2×C4×D3—28no—
456C2×C4×D3—21no—
457C2×C4×D3—21no—
458C2×C4×D3—21no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3—21no—
462C2×C4×D3C3×D411yescharacteristic
463C2×C4×D3C3×D411yescharacteristic
464C2×C4×D3C23×C311yescharacteristic
465C2×C4×D3C23×C311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C23×C311yescharacteristic
468C3×SD16—22no—
469C3×SD16—22no—
470C3×SD16—42no—
471C3×SD16—62no—
472C3×SD16—62no—
473C3×SD16—62no—
474C3×D8—22no—
475C3×D8—22no—
476C3×D8—42no—
477C3×D8—62no—
478C3×D8—62no—
479C3×D8—62no—
480C3×M16—62no—
481C3×M16—62no—
482C2×C3×C8—21no—
483C2×C3×C8—21no—
484C2×C3×C8—31no—
485C2×C3×C8—31no—
486C2×C3×C8C22×D311yescharacteristic
487C2×C3×C8C22×D311yescharacteristic
488C2×C3×C8C23×C311yescharacteristic
489C2×C3×C8C23×C311yescharacteristic
490C3×C4⋊C4—21no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—61no—
493C3×C4⋊C4C22×D311yescharacteristic
494C3×C4⋊C4C23×C311yescharacteristic
495C3×C22⋊C4—21no—
496C3×C22⋊C4—21no—
497C3×C22⋊C4—41no—
498C3×C22⋊C4—61no—
499C3×C22⋊C4—61no—
500C3×C22⋊C4—61no—
501#217—21no—
502#215—22no—
503#214—22no—
504#213—22no—
505#213—22no—
506(C2×D3)⋊C4—21no—
507(C2×D3)⋊C4—21no—
508C4⋊Dic3C23×C311yescharacteristic
509Dic3⋊C4—21no—
510C2×C3⋊C8C23×C311yescharacteristic
511C2×C3⋊C8C23×C311yescharacteristic
512D24—22no—
513#204—22no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—22no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32—41no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32C22×D411yescharacteristic
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—44no—
532C2×C3×D3—48no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—84no—
539C2×C3×D3#12012yes—
540C2×C3×D3AGL(1,ℤ/8)12yescomplemented
541C32×C4—22no—
542C32×C4—21no—
543C32×C4—41no—
544C32×C4C22×D411yescharacteristic
545C32×C4C22×D411yescharacteristic
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—31no—
553C2×#41—61no—
554C2×#41—61no—
555C2×#41—64no—
556C2×#41—64no—
557C2×#41C2×C3×D311yescharacteristic, complemented
558C22×Q8—31no—
559C22×D4—31no—
560C22×D4—31no—
561C22×D4—61no—
562C22×D4—61no—
563C23×C4—31no—
564C23×C4—61no—
565AGL(1,ℤ/8)—64no—
566AGL(1,ℤ/8)—64no—
567C2×SD16—31no—
568C2×SD16—31no—
569C2×SD16—31no—
570C2×SD16C2×C3×D311yescharacteristic, complemented
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—31no—
574C2×D8C2×C3×D311yescharacteristic, complemented
575C2×M16—31no—
576C2×M16—31no—
577#121—31no—
578#121—31no—
579#121—31no—
580#121—61no—
581#121—61no—
582#121C2×C3×D311yescharacteristic, complemented
583C2×C4⋊C4—31no—
584C2×C22⋊C4—61no—
585#103—31no—
586#103—31no—
587#103—31no—
588#103C2×C3×D311yescharacteristic, complemented
589#102—31no—
590#102—31no—
591#102—31no—
592#102C2×C3×D311yescharacteristic, complemented
593C22⋊C8—31no—
594C22⋊C8—31no—
595C22⋊C8—31no—
596C22⋊C8C2×C3×D311yescharacteristic, complemented
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—31no—
603C23×C3—31no—
604C23×C3—41no—
605C23×C3—41no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—64no—
609C23×C3—61no—
610C23×C3—61no—
611C23×C3—121no—
612C23×C3—122no—
613C23×C3—122no—
614C23×C3—122no—
615C23×C3—122no—
616C23×C3—122no—
617C23×C3D3×D411yescharacteristic
618C23×C3C2×C3×D411yescharacteristic
619C22×D3—24no—
620C22×D3—21no—
621C22×D3—22no—
622C22×D3—22no—
623C22×D3—21no—
624C22×D3—41no—
625C22×D3—42no—
626C22×D3—42no—
627C22×D3—42no—
628C22×D3—42no—
629C22×D3—42no—
630C22×D3C2×C3×D411yescharacteristic
631C22×D3C2×C3×D411yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8D3×D412yescomplemented
640C3×Q8C2×C3×D412yescomplemented
641C3×D4—24no—
642C3×D4—24no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—22no—
650C3×D4—32no—
651C3×D4—41no—
652C3×D4—41no—
653C3×D4—41no—
654C3×D4—44no—
655C3×D4—42no—
656C3×D4—42no—
657C3×D4—64no—
658C3×D4—64no—
659C3×D4—64no—
660C3×D4—64no—
661C3×D4—61no—
662C3×D4—61no—
663C3×D4—61no—
664C3×D4—82no—
665C3×D4—122no—
666C3×D4—122no—
667C3×D4—122no—
668C3×D4—122no—
669C3×D4D3×D412yescomplemented
670C3×D4C2×C3×D412yescomplemented
671C2×C3×C4—24no—
672C2×C3×C4—24no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—31no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—31no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—44no—
691C2×C3×C4—41no—
692C2×C3×C4—62no—
693C2×C3×C4—64no—
694C2×C3×C4—62no—
695C2×C3×C4—64no—
696C2×C3×C4—64no—
697C2×C3×C4—62no—
698C2×C3×C4—64no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—122no—
704C2×C3×C4D3×D411yescharacteristic
705C2×C3×C4C2×C3×D411yescharacteristic
706C2×C3×C4C23×D311yescharacteristic
707C2×C3×C4C24×C311yescharacteristic
708#67—24no—
709#67—24no—
710#67—24no—
711#67—42no—
712#67—42no—
713#67—42no—
714C2×Dic3—21no—
715C2×Dic3—22no—
716C2×Dic3—24no—
717C2×Dic3—21no—
718C2×Dic3C2×C3×D411yescharacteristic
719C2×Dic3C2×C3×D411yescharacteristic
720D12—24no—
721D12—21no—
722D12—21no—
723D12—21no—
724D12—42no—
725D12C2×C3×D412yescomplemented
726C4×D3—24no—
727C4×D3—24no—
728C4×D3—22no—
729C4×D3—21no—
730C4×D3—21no—
731C4×D3—22no—
732C4×D3—24no—
733C4×D3—42no—
734C4×D3C2×C3×D412yes—
735C4×D3C2×C3×D412yes—
736Dic6—24no—
737Dic6—21no—
738Dic6C2×C3×D412yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—41no—
744C3×C8—41no—
745C3×C8—61no—
746C3×C8—61no—
747C3⋊C8—21no—
748C3⋊C8—21no—
749C2×C32—41no—
750C2×C32—42no—
751C2×C32—81no—
752C2×C32C2×#12011yescharacteristic
753C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
754C2×C32#57511yescharacteristic
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—31no—
760C24—61no—
761C24—61no—
762#41—22no—
763#41—22no—
764#41—34no—
765#41—34no—
766#41—62no—
767#41—62no—
768#41—68no—
769#41—62no—
770#41—62no—
771#41—68no—
772C2×Q8—31no—
773C2×Q8—61no—
774C2×Q8—62no—
775C2×Q8—62no—
776C2×Q8C22×C3×D311yescharacteristic
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—31no—
780C2×D4—31no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—62no—
785C2×D4—61no—
786C2×D4—61no—
787C2×D4—62no—
788C2×D4—68no—
789C2×D4—61no—
790C2×D4—61no—
791C2×D4—62no—
792C2×D4—61no—
793C2×D4—61no—
794C2×D4—124no—
795C2×D4C22×C3×D311yescharacteristic
796C2×D4C22×C3×D311yescharacteristic
797C22×C4—21no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—68no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4C22×C3×D311yescharacteristic
812SD16—22no—
813SD16—62no—
814SD16—62no—
815SD16—62no—
816D8—22no—
817D8—62no—
818D8—62no—
819D8—62no—
820M16—62no—
821M16—62no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8C22×C3×D311yescharacteristic
825C2×C8C22×C3×D311yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—61no—
828C4⋊C4C22×C3×D311yescharacteristic
829C22⋊C4—21no—
830C22⋊C4—61no—
831C22⋊C4—61no—
832C22⋊C4—61no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—22no—
839C22×C3—21no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—32no—
843C22×C3—32no—
844C22×C3—42no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—41no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—62no—
863C22×C3—81no—
864C22×C3—81no—
865C22×C3—81no—
866C22×C3—81no—
867C22×C3—81no—
868C22×C3—124no—
869C22×C3—128no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3—244no—
876C22×C3C2×D3×D411yescharacteristic
877C22×C3C22×C3×D411yescharacteristic
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—21no—
881C2×D3—21no—
882C2×D3—22no—
883C2×D3—44no—
884C2×D3—48no—
885C2×D3—41no—
886C2×D3—41no—
887C2×D3—41no—
888C2×D3—41no—
889C2×D3—41no—
890C2×D3—84no—
891C2×D3C3×#12012yes—
892C2×D3C3×AGL(1,ℤ/8)12yescomplemented
893C3×C4—21no—
894C3×C4—22no—
895C3×C4—22no—
896C3×C4—21no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—32no—
900C3×C4—41no—
901C3×C4—42no—
902C3×C4—41no—
903C3×C4—41no—
904C3×C4—61no—
905C3×C4—62no—
906C3×C4—81no—
907C3×C4—121no—
908C3×C4C2×D3×D411yescharacteristic
909C3×C4C2×D3×D411yescharacteristic
910C3×C4C22×C3×D411yescharacteristic
911C3×C4C22×C3×D411yescharacteristic
912Dic3—21no—
913Dic3—22no—
914Dic3—41no—
915Dic3C3×#12012yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—21no—
919C23—31no—
920C23—31no—
921C23—62no—
922C23—62no—
923C23—64no—
924C23—61no—
925C23—61no—
926C23—121no—
927C23—122no—
928C23—122no—
929C23—122no—
930C23—122no—
931C23—122no—
932C23C3×D3×D411yescharacteristic
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8C3×D3×D412yescomplemented
938D4—24no—
939D4—21no—
940D4—21no—
941D4—21no—
942D4—32no—
943D4—42no—
944D4—64no—
945D4—64no—
946D4—64no—
947D4—64no—
948D4—61no—
949D4—61no—
950D4—61no—
951D4—122no—
952D4—122no—
953D4—122no—
954D4—122no—
955D4C3×D3×D412yescomplemented
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—31no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—31no—
965C2×C4—62no—
966C2×C4—64no—
967C2×C4—62no—
968C2×C4—64no—
969C2×C4—64no—
970C2×C4—62no—
971C2×C4—64no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—61no—
976C2×C4—122no—
977C2×C4C3×D3×D411yescharacteristic
978C2×C4C23×C3×D311yescharacteristic
979C8—21no—
980C8—21no—
981C8—61no—
982C8—61no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—42no—
988C2×C3—41no—
989C2×C3—42no—
990C2×C3—62no—
991C2×C3—62no—
992C2×C3—81no—
993C2×C3—82no—
994C2×C3—81no—
995C2×C3—81no—
996C2×C3—122no—
997C2×C3—161no—
998C2×C3—241no—
999C2×C3D3×#12011yescharacteristic
1000C2×C3#576811yescharacteristic
1001C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1002C2×C3C2×C3×#12011yescharacteristic
1003C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
1004C2×C3C3×#57511yescharacteristic
1005D3—22no—
1006D3—22no—
1007D3—42no—
1008D3—81no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—22no—
1013C22—32no—
1014C22—32no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—61no—
1021C22—61no—
1022C22—61no—
1023C22—61no—
1024C22—62no—
1025C22—124no—
1026C22—128no—
1027C22—121no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—121no—
1032C22—244no—
1033C22C2×C3×D3×D411yescharacteristic
1034C4—21no—
1035C4—22no—
1036C4—32no—
1037C4—41no—
1038C4—61no—
1039C4—62no—
1040C4—121no—
1041C4C2×C3×D3×D411yescharacteristic
1042C4C2×C3×D3×D411yescharacteristic
1043C3—21no—
1044C3#8008411yescharacteristic, direct product factor
1045C3C3×#300611yescharacteristic, complemented
1046C2—41no—
1047C2—42no—
1048C2—62no—
1049C2—62no—
1050C2—81no—
1051C2—122no—
1052C2—241no—
1053C2C3×D3×#12011yescharacteristic
1054C2C3×#576811yescharacteristic
1055C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3006
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×C3×#914C2semidirect
3. C2×C3×#911C2semidirect
4. C3×D3×#121C2semidirect
5. C32×#449C2semidirect
6. C3×#5238C2semidirect
7. C3×#5170C2semidirect
8. C3×#5156C2semidirect
9. C3×#5037C2semidirect
10. C3×#4806C2semidirect
11. C3×#4803C2semidirect
12. C3×#4773C2semidirect
13. C3×#4771C2semidirect
14. C3×#4734C2semidirect
15. C3×#4726C2semidirect
17. #80084C3direct (N × H)
18. C2×C32×#41C22semidirect
22. C2×C3×D3×Q8C22semidirect
27. C2×C3×D3×D4C22semidirect
28. C2×C3×D3×D4C22semidirect
30. C2×C3×#235C22semidirect
33. C2×C32×SD16C22semidirect
34. C2×C32×D8C22semidirect
35. C32×#121C22semidirect
36. C2×C3×#215C22semidirect
39. C2×C3×#214C22semidirect
40. C2×C3×#213C22semidirect
41. C2×C3×#213C22semidirect
42. C3×#930C22semidirect
45. C2×C3×D24C22semidirect
46. C2×C3×#204C22semidirect
47. C2×C3×ΓL(1,𝔽25)C22semidirect
48. C2×C3×ΓL(1,𝔽25)C22semidirect
50. C3×D3×C4⋊C4C22semidirect
53. C32×#103C22semidirect
54. C32×#102C22semidirect
55. C32×C22⋊C8C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. C3×#821C22semidirect
60. C3×(C2×D3)⋊C8C22semidirect
61. C3×(C2×D3)⋊C8C22semidirect
62. C3×#816C22semidirect
63. C3×#810C22semidirect
64. C3×#809C22semidirect
66. C2×D3×#41C2×C3semidirect
70. C2×#914C2×C3semidirect
71. C2×#911C2×C3semidirect
72. D3×#121C2×C3semidirect
77. C3×#449D3semidirect
78. C3×#449C2×C3semidirect
86. #5238C2×C3semidirect
87. #5170C2×C3semidirect
88. #5156C2×C3semidirect
89. #5037C2×C3semidirect
90. #4806C2×C3semidirect
91. #4803C2×C3semidirect
92. #4773C2×C3semidirect
93. #4771C2×C3semidirect
94. #4734C2×C3semidirect
95. #4726C2×C3semidirect
117. C3×#239D4semidirect
122. C3×#237D4semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C22×C3semidirect
191. C2×D3×Q8C22×C3semidirect
196. C2×D3×D4C22×C3semidirect
197. C2×D3×D4C22×C3semidirect
199. C2×#235C22×C3semidirect
208. C2×C3×SD16C2×D3semidirect
209. C2×C3×SD16C22×C3semidirect
214. C2×C3×D8C2×D3semidirect
215. C2×C3×D8C22×C3semidirect
224. C3×#121C2×D3semidirect
225. C3×#121C22×C3semidirect
228. C2×#215C22×C3semidirect
231. C2×#214C22×C3semidirect
232. C2×#213C22×C3semidirect
233. C2×#213C22×C3semidirect
234. #930C22×C3semidirect
237. C2×D24C22×C3semidirect
238. C2×#204C22×C3semidirect
239. C2×ΓL(1,𝔽25)C22×C3semidirect
240. C2×ΓL(1,𝔽25)C22×C3semidirect
242. D3×C4⋊C4C22×C3semidirect
249. C3×#103C2×D3semidirect
250. C3×#103C22×C3semidirect
255. C3×#102C2×D3semidirect
256. C3×#102C22×C3semidirect
261. C3×C22⋊C8C2×D3semidirect
262. C3×C22⋊C8C22×C3semidirect
263. #835C22×C3semidirect
264. #832C22×C3semidirect
265. #830C22×C3semidirect
266. #821C22×C3semidirect
267. (C2×D3)⋊C8C22×C3semidirect
268. (C2×D3)⋊C8C22×C3semidirect
269. #816C22×C3semidirect
270. #810C22×C3semidirect
271. #809C22×C3semidirect
289. C32×Q8C2×D4semidirect
295. C32×D4C2×D4semidirect
320. C3×D12C2×D4semidirect
333. C3×Dic6C2×D4semidirect
345. #449C3×D3semidirect
436. #239C3×D4semidirect
441. #237C3×D4semidirect
540. C2×C3×D3AGL(1,ℤ/8)semidirect
557. C2×#41C2×C3×D3semidirect
570. C2×SD16C2×C3×D3semidirect
574. C2×D8C2×C3×D3semidirect
582. #121C2×C3×D3semidirect
588. #103C2×C3×D3semidirect
592. #102C2×C3×D3semidirect
596. C22⋊C8C2×C3×D3semidirect
639. C3×Q8D3×D4semidirect
640. C3×Q8C2×C3×D4semidirect
669. C3×D4D3×D4semidirect
670. C3×D4C2×C3×D4semidirect
725. D12C2×C3×D4semidirect
738. Dic6C2×C3×D4semidirect
892. C2×D3C3×AGL(1,ℤ/8)semidirect
916. C32#3006semidirect
937. Q8C3×D3×D4semidirect
955. D4C3×D3×D4semidirect
1044. C3#80084direct (N × H)
1045. C3C3×#3006semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×#9142
C2×C3×#9112
C3×D3×#1212
C32×#4492
C3×#52382
C3×#51702
C3×#51562
C3×#50372
C3×#48062
C3×#48032
C3×#47732
C3×#47712
C3×#47342
C3×#47262
C3×#30063
#800843