Finite Group Databasebeta

← C3×#80228 #11864178

Subgroups — C3×#80228 #11864178

Order 1152.

1584 conjugacy classes of subgroups.

The subgroup lattice has 997 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C3×#918C211yesmaximal, characteristic, complemented
3C2×C3×#915C211yesmaximal, characteristic, complemented
4C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
5C32×#452C211yesmaximal, characteristic, complemented
6C3×#5239C211yesmaximal, characteristic, complemented
7C3×#5186C211yesmaximal, characteristic, complemented
8C3×#5169C211yesmaximal, characteristic, complemented
9C3×#5047C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×#4803C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×#4771C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4726C211yesmaximal, characteristic, complemented
16C3×#3007—31nomaximal
17#80228C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237—21no—
25C2×C3×#237C2211yescharacteristic
26C2×C3×D3×D4—21no—
27C2×C3×D3×D4C2211yescharacteristic
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C22×C3×C4×D3—21no—
31C22×C3×C4×D3C2211yescharacteristic
32C2×C32×Q16C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34C32×C22⋊Q8C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#216C2211yescharacteristic, complemented
38C2×C3×#215C2211yescharacteristic, complemented
39C2×C3×#214C2211yescharacteristic, complemented
40C3×#924C2211yescharacteristic, complemented
41C3×#918—24no—
42C3×#915—24no—
43C2×C3×Dic12C2211yescharacteristic, complemented
44C2×C3×#204C2211yescharacteristic, complemented
45C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
46C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
47C3×#897C2211yescharacteristic
48C3×#896—21no—
49C3×D3×C4⋊C4—21no—
50C3×D3×C4⋊C4C2211yescharacteristic, complemented
51C3×D3×C22⋊C4—21no—
52C3×#878—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
61C3×(C2×D3)⋊C8C2211yescharacteristic
62C3×#816C2211yescharacteristic, complemented
63C3×#810C2211yescharacteristic, complemented
64C3×#809C2211yescharacteristic, complemented
65C22×C3×#41—31no—
66C2×D3×#41C2×C311yescharacteristic
67C2×C3×#137—31no—
68C2×C3×#137—31no—
69C2×C3×C22⋊Q8—31no—
70C2×#918C2×C311yescharacteristic, complemented
71C2×#915C2×C311yescharacteristic, complemented
72D3×C22⋊Q8C2×C311yescharacteristic, complemented
73C3×#452—21no—
74C3×#452—31no—
75C3×#452—31no—
76C3×#452—31no—
77C3×#452D311yescharacteristic, complemented
78C3×#452C2×C311yescharacteristic, complemented
79C3×#451—31no—
80C3×#451—31no—
81C3×#450—31no—
82C3×#450—31no—
83C3×#417—31no—
84C3×#417—31no—
85C3×#407—31no—
86#5239C2×C311yescharacteristic, complemented
87#5186C2×C311yescharacteristic, complemented
88#5169C2×C311yescharacteristic, complemented
89#5047C2×C311yescharacteristic, complemented
90#4809C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92#4776C2×C311yescharacteristic, complemented
93#4771C2×C311yescharacteristic, complemented
94#4733C2×C311yescharacteristic, complemented
95#4726C2×C311yescharacteristic, complemented
96C23×C3×D3—21no—
97C23×C3×D3D411yescharacteristic
98C32×#41—22no—
99C32×#41—22no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3D411yescharacteristic
111C3×#239—22no—
112C3×#239D414yes—
113C3×D3×Q8—22no—
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C3×#237—28no—
118C3×#237—22no—
119C3×#237D414yes—
120C3×D3×D4—28no—
121C3×D3×D4—22no—
122C3×D3×D4—22no—
123C3×#235—28no—
124C3×#235—22no—
125C3×#235—22no—
126C2×C3×D12—21no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3—28no—
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3—22no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3D411yescharacteristic
137C2×C3×C4×D3D411yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6—21no—
141C2×C3×Dic6—21no—
142C2×C3×Dic6C2311yescharacteristic
143C2×C3×Dic6C2311yescharacteristic
144C32×Q16—22no—
145C32×SD16—22no—
146C2×C32×C8C2311yescharacteristic
147C2×C32×C8C2311yescharacteristic
148C32×C4⋊C4—21no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C22⋊C4—21no—
151C3×#217—21no—
152C3×#216—22no—
153C3×#216—22no—
154C3×#215—22no—
155C3×#214—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3—21no—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×Dic3⋊C4—21no—
161C3×Dic3⋊C4—21no—
162C3×Dic3⋊C4—21no—
163C2×C3×C3⋊C8C2311yescharacteristic
164C2×C3×C3⋊C8C2311yescharacteristic
165C3×Dic12—22no—
166C3×#204—22no—
167C3×ΓL(1,𝔽25)—22no—
168C3×ΓL(1,𝔽25)—22no—
169#3007—31noSylow
170C2×C3×#41—21no—
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—61no—
175C2×C3×#41—61no—
176C2×C3×#41—64no—
177C2×C3×#41—64no—
178C2×C3×#41C2×D311yescharacteristic
179C2×C3×#41C22×C311yescharacteristic
180C22×C3×Q8—31no—
181C22×C3×Q8—31no—
182C22×C3×D4—31no—
183C22×C3×D4—61no—
184C23×C3×C4—31no—
185C23×C3×C4—61no—
186D3×#41—24no—
187D3×#41—24no—
188C2×#239C22×C311yescharacteristic
189C2×D3×Q8C22×C311yescharacteristic
190C2×D3×Q8C22×C311yescharacteristic, complemented
191C2×#237—21no—
192C2×#237C22×C311yescharacteristic
193C2×D3×D4—21no—
194C2×D3×D4C22×C311yescharacteristic
195C2×#235—21no—
196C2×#235C22×C311yescharacteristic
197C22×C4×D3—21no—
198C22×C4×D3C22×C311yescharacteristic
199C3×#137—64no—
200C3×#137—64no—
201C2×C3×Q16—21no—
202C2×C3×Q16—31no—
203C2×C3×Q16—31no—
204C2×C3×Q16—31no—
205C2×C3×Q16C2×D311yescharacteristic, complemented
206C2×C3×Q16C22×C311yescharacteristic, complemented
207C2×C3×SD16—21no—
208C2×C3×SD16—31no—
209C2×C3×SD16—31no—
210C2×C3×SD16—31no—
211C2×C3×SD16C2×D311yescharacteristic, complemented
212C2×C3×SD16C22×C311yescharacteristic, complemented
213C2×C3×M16—31no—
214C2×C3×M16—31no—
215C3×C22⋊Q8—21no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—31no—
218C3×C22⋊Q8—31no—
219C3×C22⋊Q8—61no—
220C3×C22⋊Q8—61no—
221C3×C22⋊Q8C2×D311yescharacteristic, complemented
222C3×C22⋊Q8C22×C311yescharacteristic, complemented
223C2×C3×C4⋊C4—31no—
224C2×C3×C4⋊C4—61no—
225C2×C3×C22⋊C4—61no—
226#946C22×C311yescharacteristic
227C2×#216C22×C311yescharacteristic, complemented
228C2×#216C22×C311yescharacteristic, complemented
229C2×#215C22×C311yescharacteristic, complemented
230C2×#214C22×C311yescharacteristic, complemented
231#924C22×C311yescharacteristic, complemented
232#918—24no—
233#915—24no—
234C2×Dic12C22×C311yescharacteristic, complemented
235C2×#204C22×C311yescharacteristic, complemented
236C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
237C2×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
238#897C22×C311yescharacteristic
239#896—21no—
240D3×C4⋊C4—21no—
241D3×C4⋊C4C22×C311yescharacteristic, complemented
242D3×C22⋊C4—21no—
243#878—21no—
244C3×#103—21no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#103—31no—
248C3×#103C2×D311yescharacteristic, complemented
249C3×#103C22×C311yescharacteristic, complemented
250C3×#102—21no—
251C3×#102—31no—
252C3×#102—31no—
253C3×#102—31no—
254C3×#102C2×D311yescharacteristic, complemented
255C3×#102C22×C311yescharacteristic, complemented
256C3×C22⋊C8—21no—
257C3×C22⋊C8—31no—
258C3×C22⋊C8—31no—
259C3×C22⋊C8—31no—
260C3×C22⋊C8C2×D311yescharacteristic, complemented
261C3×C22⋊C8C22×C311yescharacteristic, complemented
262#835C22×C311yescharacteristic, complemented
263#832C22×C311yescharacteristic, complemented
264#830C22×C311yescharacteristic, complemented
265#821C22×C311yescharacteristic, complemented
266(C2×D3)⋊C8C22×C311yescharacteristic
267(C2×D3)⋊C8C22×C311yescharacteristic
268#816C22×C311yescharacteristic, complemented
269#810C22×C311yescharacteristic, complemented
270#809C22×C311yescharacteristic, complemented
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—24no—
274C22×C3×D3—21no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—41no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C32×Q8—21no—
283C32×Q8—21no—
284C32×Q8—21no—
285C32×Q8C2×D412yes—
286C32×D4—24no—
287C32×D4—21no—
288C32×D4C2×D412yes—
289C2×C32×C4—24no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4C2×D411yescharacteristic
296C2×C32×C4C2411yescharacteristic
297C3×#67—24no—
298C3×#67—24no—
299C3×#67—24no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—24no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3C2×D411yescharacteristic
306C2×C3×Dic3C2×D411yescharacteristic
307C3×D12—24no—
308C3×D12—21no—
309C3×D12C2×D412yes—
310C3×C4×D3—24no—
311C3×C4×D3—24no—
312C3×C4×D3—22no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3—22no—
316C3×C4×D3—24no—
317C3×C4×D3—42no—
318C3×C4×D3—42no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321C3×Dic6—24no—
322C3×Dic6—21no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—42no—
326C3×Dic6C2×D412yes—
327C32×C8—21no—
328C32×C8—21no—
329C3×C3⋊C8—21no—
330C3×C3⋊C8—21no—
331C22×#41—31no—
332C2×#137—31no—
333C2×#137—31no—
334C2×C22⋊Q8—31no—
335#452—31no—
336#452—31no—
337#452—31no—
338#452C3×D311yescharacteristic, complemented
339#451—31no—
340#451—31no—
341#450—31no—
342#450—31no—
343#417—31no—
344#417—31no—
345#407—31no—
346C24×C3—31no—
347C24×C3—61no—
348C23×D3—21no—
349C23×D3C3×D411yescharacteristic
350C3×#41—22no—
351C3×#41—22no—
352C3×#41—22no—
353C3×#41—22no—
354C3×#41—34no—
355C3×#41—34no—
356C3×#41—42no—
357C3×#41—42no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—68no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—68no—
364C2×C3×Q8—21no—
365C2×C3×Q8—21no—
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×Q8—61no—
369C2×C3×Q8—61no—
370C2×C3×Q8—62no—
371C2×C3×Q8—62no—
372C2×C3×Q8—62no—
373C2×C3×Q8—62no—
374C2×C3×Q8C22×D311yescharacteristic
375C2×C3×Q8C22×D311yescharacteristic
376C2×C3×Q8C23×C311yescharacteristic
377C2×C3×Q8C23×C311yescharacteristic
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—31no—
382C2×C3×D4—41no—
383C2×C3×D4—61no—
384C2×C3×D4—61no—
385C2×C3×D4—62no—
386C2×C3×D4—68no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—62no—
390C2×C3×D4C22×D311yescharacteristic
391C2×C3×D4C23×C311yescharacteristic
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—41no—
401C22×C3×C4—62no—
402C22×C3×C4—62no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—68no—
406C22×C3×C4—61no—
407C22×C3×C4—61no—
408C22×C3×C4—61no—
409C22×C3×C4—61no—
410C22×C3×C4C22×D311yescharacteristic
411C22×C3×C4C23×C311yescharacteristic
412C2×#67—21no—
413C2×#67—21no—
414C2×#67—21no—
415C22×Dic3—21no—
416C22×Dic3C3×D411yescharacteristic
417#239—22no—
418#239C3×D414yes—
419D3×Q8—22no—
420D3×Q8—22no—
421D3×Q8—22no—
422D3×Q8—22no—
423#237—28no—
424#237—22no—
425#237C3×D414yes—
426D3×D4—28no—
427D3×D4—22no—
428D3×D4—22no—
429#235—28no—
430#235—22no—
431#235—22no—
432C2×D12—21no—
433C2×D12C23×C311yescharacteristic
434C2×C4×D3—28no—
435C2×C4×D3—21no—
436C2×C4×D3—21no—
437C2×C4×D3—21no—
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—21no—
441C2×C4×D3—21no—
442C2×C4×D3C3×D411yescharacteristic
443C2×C4×D3C3×D411yescharacteristic
444C2×C4×D3C23×C311yescharacteristic
445C2×C4×D3C23×C311yescharacteristic
446C2×Dic6—21no—
447C2×Dic6—21no—
448C2×Dic6C23×C311yescharacteristic
449C2×Dic6C23×C311yescharacteristic
450C3×Q16—22no—
451C3×Q16—22no—
452C3×Q16—42no—
453C3×Q16—62no—
454C3×Q16—62no—
455C3×Q16—62no—
456C3×SD16—22no—
457C3×SD16—22no—
458C3×SD16—42no—
459C3×SD16—62no—
460C3×SD16—62no—
461C3×SD16—62no—
462C3×M16—62no—
463C3×M16—62no—
464C2×C3×C8—21no—
465C2×C3×C8—21no—
466C2×C3×C8—31no—
467C2×C3×C8—31no—
468C2×C3×C8C22×D311yescharacteristic
469C2×C3×C8C22×D311yescharacteristic
470C2×C3×C8C23×C311yescharacteristic
471C2×C3×C8C23×C311yescharacteristic
472C3×C4⋊C4—21no—
473C3×C4⋊C4—21no—
474C3×C4⋊C4—21no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—41no—
477C3×C4⋊C4—61no—
478C3×C4⋊C4—61no—
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#217—21no—
490#216—22no—
491#216—22no—
492#215—22no—
493#214—22no—
494(C2×D3)⋊C4—21no—
495(C2×D3)⋊C4—21no—
496C4⋊Dic3—21no—
497C4⋊Dic3C23×C311yescharacteristic
498Dic3⋊C4—21no—
499Dic3⋊C4—21no—
500Dic3⋊C4—21no—
501C2×C3⋊C8C23×C311yescharacteristic
502C2×C3⋊C8C23×C311yescharacteristic
503Dic12—22no—
504#204—22no—
505ΓL(1,𝔽25)—22no—
506ΓL(1,𝔽25)—22no—
507C22×C32—21no—
508C22×C32—22no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32—41no—
512C22×C32—41no—
513C22×C32C22×D411yescharacteristic
514C2×C3×D3—21no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—44no—
520C2×C3×D3—48no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3#12012yes—
524C2×C3×D3#13712yescomplemented
525C32×C4—22no—
526C32×C4—21no—
527C32×C4—41no—
528C32×C4—41no—
529C32×C4C22×D411yescharacteristic
530C32×C4C22×D411yescharacteristic
531C3×Dic3—21no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3#12012yes—
536C2×#41—31no—
537C2×#41—31no—
538C2×#41—31no—
539C2×#41—61no—
540C2×#41—61no—
541C2×#41—64no—
542C2×#41—64no—
543C2×#41C2×C3×D311yescharacteristic
544C22×Q8—31no—
545C22×Q8—31no—
546C22×D4—31no—
547C22×D4—61no—
548C23×C4—31no—
549C23×C4—61no—
550#137—64no—
551#137—64no—
552C2×Q16—31no—
553C2×Q16—31no—
554C2×Q16—31no—
555C2×Q16C2×C3×D311yescharacteristic, complemented
556C2×SD16—31no—
557C2×SD16—31no—
558C2×SD16—31no—
559C2×SD16C2×C3×D311yescharacteristic, complemented
560C2×M16—31no—
561C2×M16—31no—
562C22⋊Q8—31no—
563C22⋊Q8—31no—
564C22⋊Q8—31no—
565C22⋊Q8—61no—
566C22⋊Q8—61no—
567C22⋊Q8C2×C3×D311yescharacteristic, complemented
568C2×C4⋊C4—31no—
569C2×C4⋊C4—61no—
570C2×C22⋊C4—61no—
571#103—31no—
572#103—31no—
573#103—31no—
574#103C2×C3×D311yescharacteristic, complemented
575#102—31no—
576#102—31no—
577#102—31no—
578#102C2×C3×D311yescharacteristic, complemented
579C22⋊C8—31no—
580C22⋊C8—31no—
581C22⋊C8—31no—
582C22⋊C8C2×C3×D311yescharacteristic, complemented
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—21no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—41no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—64no—
592C23×C3—61no—
593C23×C3—121no—
594C23×C3—122no—
595C23×C3—122no—
596C23×C3D3×D411yescharacteristic
597C23×C3C2×C3×D411yescharacteristic
598C22×D3—24no—
599C22×D3—21no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—41no—
603C22×D3—42no—
604C22×D3—42no—
605C22×D3C2×C3×D411yescharacteristic
606C22×D3C2×C3×D411yescharacteristic
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—22no—
614C3×Q8—32no—
615C3×Q8—41no—
616C3×Q8—41no—
617C3×Q8—41no—
618C3×Q8—64no—
619C3×Q8—61no—
620C3×Q8—61no—
621C3×Q8—61no—
622C3×Q8—122no—
623C3×Q8D3×D412yes—
624C3×Q8C2×C3×D412yes—
625C3×D4—24no—
626C3×D4—24no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—22no—
630C3×D4—32no—
631C3×D4—41no—
632C3×D4—44no—
633C3×D4—64no—
634C3×D4—64no—
635C3×D4—64no—
636C3×D4—64no—
637C3×D4—61no—
638C3×D4D3×D412yes—
639C3×D4C2×C3×D412yes—
640C2×C3×C4—24no—
641C2×C3×C4—24no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—31no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—31no—
658C2×C3×C4—41no—
659C2×C3×C4—41no—
660C2×C3×C4—41no—
661C2×C3×C4—44no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—62no—
665C2×C3×C4—64no—
666C2×C3×C4—62no—
667C2×C3×C4—64no—
668C2×C3×C4—64no—
669C2×C3×C4—62no—
670C2×C3×C4—64no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—122no—
677C2×C3×C4—122no—
678C2×C3×C4D3×D411yescharacteristic
679C2×C3×C4C2×C3×D411yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C24×C311yescharacteristic
682#67—24no—
683#67—24no—
684#67—24no—
685C2×Dic3—21no—
686C2×Dic3—22no—
687C2×Dic3—24no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3C2×C3×D411yescharacteristic
691C2×Dic3C2×C3×D411yescharacteristic
692D12—24no—
693D12—21no—
694D12C2×C3×D412yes—
695C4×D3—24no—
696C4×D3—24no—
697C4×D3—22no—
698C4×D3—21no—
699C4×D3—21no—
700C4×D3—22no—
701C4×D3—24no—
702C4×D3—42no—
703C4×D3—42no—
704C4×D3C2×C3×D412yes—
705C4×D3C2×C3×D412yes—
706Dic6—24no—
707Dic6—21no—
708Dic6—21no—
709Dic6—21no—
710Dic6—42no—
711Dic6C2×C3×D412yes—
712C3×C8—21no—
713C3×C8—21no—
714C3×C8—21no—
715C3×C8—21no—
716C3×C8—41no—
717C3×C8—41no—
718C3×C8—61no—
719C3×C8—61no—
720C3⋊C8—21no—
721C3⋊C8—21no—
722C2×C32—41no—
723C2×C32—42no—
724C2×C32C2×#12011yescharacteristic
725C2×C32C2×#13711yescharacteristic
726C2×C32#57511yescharacteristic
727C3×D3—22no—
728C3×D3—22no—
729C3×D3—42no—
730C24—31no—
731C24—61no—
732#41—22no—
733#41—22no—
734#41—34no—
735#41—34no—
736#41—62no—
737#41—62no—
738#41—68no—
739#41—62no—
740#41—62no—
741#41—68no—
742C2×Q8—31no—
743C2×Q8—31no—
744C2×Q8—61no—
745C2×Q8—61no—
746C2×Q8—62no—
747C2×Q8—62no—
748C2×Q8—62no—
749C2×Q8—62no—
750C2×Q8C22×C3×D311yescharacteristic
751C2×Q8C22×C3×D311yescharacteristic
752C2×D4—21no—
753C2×D4—31no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—62no—
757C2×D4—68no—
758C2×D4—61no—
759C2×D4—61no—
760C2×D4—62no—
761C2×D4C22×C3×D311yescharacteristic
762C22×C4—21no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—62no—
769C22×C4—62no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—68no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4C22×C3×D311yescharacteristic
778Q16—22no—
779Q16—62no—
780Q16—62no—
781Q16—62no—
782SD16—22no—
783SD16—62no—
784SD16—62no—
785SD16—62no—
786M16—62no—
787M16—62no—
788C2×C8—31no—
789C2×C8—31no—
790C2×C8C22×C3×D311yescharacteristic
791C2×C8C22×C3×D311yescharacteristic
792C4⋊C4—21no—
793C4⋊C4—31no—
794C4⋊C4—61no—
795C4⋊C4—61no—
796C4⋊C4—61no—
797C4⋊C4—61no—
798C4⋊C4C22×C3×D311yescharacteristic
799C22⋊C4—21no—
800C22⋊C4—61no—
801C22⋊C4—61no—
802C22⋊C4—61no—
803C22×C3—21no—
804C22×C3—21no—
805C22×C3—21no—
806C22×C3—21no—
807C22×C3—21no—
808C22×C3—22no—
809C22×C3—21no—
810C22×C3—22no—
811C22×C3—21no—
812C22×C3—32no—
813C22×C3—32no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—62no—
827C22×C3—81no—
828C22×C3—81no—
829C22×C3—124no—
830C22×C3—128no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3C2×D3×D411yescharacteristic
834C22×C3C22×C3×D411yescharacteristic
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—21no—
839C2×D3—22no—
840C2×D3—44no—
841C2×D3—48no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3C3×#12012yes—
845C2×D3C3×#13712yescomplemented
846C3×C4—21no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—21no—
850C3×C4—21no—
851C3×C4—21no—
852C3×C4—32no—
853C3×C4—41no—
854C3×C4—42no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—41no—
858C3×C4—41no—
859C3×C4—61no—
860C3×C4—62no—
861C3×C4—81no—
862C3×C4—81no—
863C3×C4—121no—
864C3×C4—121no—
865C3×C4C2×D3×D411yescharacteristic
866C3×C4C2×D3×D411yescharacteristic
867C3×C4C22×C3×D411yescharacteristic
868C3×C4C22×C3×D411yescharacteristic
869Dic3—21no—
870Dic3—22no—
871Dic3—41no—
872Dic3—41no—
873Dic3C3×#12012yes—
874C32#300711yescharacteristic, complemented, Sylow
875C23—21no—
876C23—31no—
877C23—31no—
878C23—62no—
879C23—62no—
880C23—64no—
881C23—61no—
882C23—121no—
883C23—122no—
884C23—122no—
885C23C3×D3×D411yescharacteristic
886Q8—21no—
887Q8—21no—
888Q8—21no—
889Q8—32no—
890Q8—64no—
891Q8—61no—
892Q8—61no—
893Q8—61no—
894Q8—122no—
895Q8C3×D3×D412yes—
896D4—24no—
897D4—21no—
898D4—32no—
899D4—64no—
900D4—64no—
901D4—64no—
902D4—64no—
903D4—61no—
904D4C3×D3×D412yes—
905C2×C4—24no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—31no—
912C2×C4—32no—
913C2×C4—32no—
914C2×C4—31no—
915C2×C4—62no—
916C2×C4—64no—
917C2×C4—62no—
918C2×C4—64no—
919C2×C4—64no—
920C2×C4—62no—
921C2×C4—64no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—122no—
928C2×C4—122no—
929C2×C4C3×D3×D411yescharacteristic
930C2×C4C23×C3×D311yescharacteristic
931C8—21no—
932C8—21no—
933C8—61no—
934C8—61no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—41no—
939C2×C3—42no—
940C2×C3—41no—
941C2×C3—42no—
942C2×C3—62no—
943C2×C3—62no—
944C2×C3—81no—
945C2×C3—82no—
946C2×C3—122no—
947C2×C3D3×#12011yescharacteristic
948C2×C3#576811yescharacteristic
949C2×C3D3×#13711yescharacteristic
950C2×C3C2×C3×#12011yescharacteristic
951C2×C3C2×C3×#13711yescharacteristic
952C2×C3C3×#57511yescharacteristic
953D3—22no—
954D3—22no—
955D3—42no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—32no—
961C22—32no—
962C22—41no—
963C22—41no—
964C22—61no—
965C22—61no—
966C22—61no—
967C22—61no—
968C22—62no—
969C22—124no—
970C22—128no—
971C22—121no—
972C22—121no—
973C22C2×C3×D3×D411yescharacteristic
974C4—21no—
975C4—22no—
976C4—32no—
977C4—41no—
978C4—41no—
979C4—61no—
980C4—62no—
981C4—121no—
982C4—121no—
983C4C2×C3×D3×D411yescharacteristic
984C4C2×C3×D3×D411yescharacteristic
985C3—21no—
986C3#8022811yescharacteristic, direct product factor
987C3C3×#300711yescharacteristic, complemented
988C2—41no—
989C2—42no—
990C2—62no—
991C2—62no—
992C2—122no—
993C2C3×D3×#12011yescharacteristic
994C2C3×#576811yescharacteristic
995C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
hypercenterC3×#452D3
hypocenterC3C3×#3007
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
2. C2×C3×#918C2semidirect
3. C2×C3×#915C2semidirect
4. C3×D3×C22⋊Q8C2semidirect
5. C32×#452C2semidirect
6. C3×#5239C2semidirect
7. C3×#5186C2semidirect
8. C3×#5169C2semidirect
9. C3×#5047C2semidirect
10. C3×#4809C2semidirect
11. C3×#4803C2semidirect
12. C3×#4776C2semidirect
13. C3×#4771C2semidirect
14. C3×#4733C2semidirect
15. C3×#4726C2semidirect
17. #80228C3direct (N × H)
23. C2×C3×D3×Q8C22semidirect
32. C2×C32×Q16C22semidirect
33. C2×C32×SD16C22semidirect
34. C32×C22⋊Q8C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#216C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#214C22semidirect
40. C3×#924C22semidirect
43. C2×C3×Dic12C22semidirect
44. C2×C3×#204C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. 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
62. C3×#816C22semidirect
63. C3×#810C22semidirect
64. C3×#809C22semidirect
70. C2×#918C2×C3semidirect
71. C2×#915C2×C3semidirect
72. D3×C22⋊Q8C2×C3semidirect
77. C3×#452D3semidirect
78. C3×#452C2×C3semidirect
86. #5239C2×C3semidirect
87. #5186C2×C3semidirect
88. #5169C2×C3semidirect
89. #5047C2×C3semidirect
90. #4809C2×C3semidirect
91. #4803C2×C3semidirect
92. #4776C2×C3semidirect
93. #4771C2×C3semidirect
94. #4733C2×C3semidirect
95. #4726C2×C3semidirect
190. C2×D3×Q8C22×C3semidirect
205. C2×C3×Q16C2×D3semidirect
206. C2×C3×Q16C22×C3semidirect
211. C2×C3×SD16C2×D3semidirect
212. C2×C3×SD16C22×C3semidirect
221. C3×C22⋊Q8C2×D3semidirect
222. C3×C22⋊Q8C22×C3semidirect
227. C2×#216C22×C3semidirect
228. C2×#216C22×C3semidirect
229. C2×#215C22×C3semidirect
230. C2×#214C22×C3semidirect
231. #924C22×C3semidirect
234. C2×Dic12C22×C3semidirect
235. C2×#204C22×C3semidirect
236. C2×ΓL(1,𝔽25)C22×C3semidirect
237. C2×ΓL(1,𝔽25)C22×C3semidirect
241. D3×C4⋊C4C22×C3semidirect
248. C3×#103C2×D3semidirect
249. C3×#103C22×C3semidirect
254. C3×#102C2×D3semidirect
255. C3×#102C22×C3semidirect
260. C3×C22⋊C8C2×D3semidirect
261. C3×C22⋊C8C22×C3semidirect
262. #835C22×C3semidirect
263. #832C22×C3semidirect
264. #830C22×C3semidirect
265. #821C22×C3semidirect
268. #816C22×C3semidirect
269. #810C22×C3semidirect
270. #809C22×C3semidirect
338. #452C3×D3semidirect
524. C2×C3×D3#137semidirect
555. C2×Q16C2×C3×D3semidirect
559. C2×SD16C2×C3×D3semidirect
567. C22⋊Q8C2×C3×D3semidirect
574. #103C2×C3×D3semidirect
578. #102C2×C3×D3semidirect
582. C22⋊C8C2×C3×D3semidirect
845. C2×D3C3×#137semidirect
874. C32#3007semidirect
986. C3#80228direct (N × H)
987. C3C3×#3007semidirect

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×#9182
C2×C3×#9152
C3×D3×C22⋊Q82
C32×#4522
C3×#52392
C3×#51862
C3×#51692
C3×#50472
C3×#48092
C3×#48032
C3×#47762
C3×#47712
C3×#47332
C3×#47262
C3×#30073
#802283