Finite Group Databasebeta

← C3×#10594400 #13173959

Subgroups — C3×#10594400 #13173959

Order 1728.

1048 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64105C211yesmaximal, characteristic
2C32×#889C211yesmaximal, characteristic, complemented
3C32×#888C211yesmaximal, characteristic, complemented
4C3×#63895C211yesmaximal, characteristic
5C3×#63888C211yesmaximal, characteristic
6C3×#63883C211yesmaximal, characteristic
7C3×#63871C211yesmaximal, characteristic
8C3×#63867C211yesmaximal, characteristic, complemented
9C3×#63866C211yesmaximal, characteristic, complemented
10C3×#63846C211yesmaximal, characteristic, complemented
11C3×#63846C211yesmaximal, characteristic, complemented
12C3×#63840C211yesmaximal, characteristic, complemented
13C3×#63839C211yesmaximal, characteristic, complemented
14C3×#63836C211yesmaximal, characteristic
15C3×#63836C211yesmaximal, characteristic
16C3×#5729—31nomaximal
17C3×#5689—31nomaximal
18#10594400C311yesmaximal, characteristic, direct product factor
19C2×C3×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#624C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3752C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C3×#3724C2211yescharacteristic
42C3×Dic3⋊Dic3C2211yescharacteristic
43C3×Dic3⋊Dic3C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×C4⋊Q8—31no—
55C32×#125—31no—
56#64105C2×C311yescharacteristic
57C3×#946—31no—
58C3×#946—31no—
59C3×#944—31no—
60C3×#944—31no—
61C3×#897—31no—
62C3×#897—31no—
63C3×#896—31no—
64C3×#896—31no—
65C3×#896—31no—
66C3×#896—31no—
67C3×#896—61no—
68C3×#892—31no—
69C3×#892—31no—
70C3×D3×C4⋊C4—31no—
71C3×D3×C4⋊C4—31no—
72C3×#890—31no—
73C3×#890—31no—
74C3×#889—21no—
75C3×#889—31no—
76C3×#889—31no—
77C3×#889—31no—
78C3×#889D311yescharacteristic, complemented
79C3×#889C2×C311yescharacteristic, complemented
80C3×#888—21no—
81C3×#888—31no—
82C3×#888—31no—
83C3×#888—31no—
84C3×#888D311yescharacteristic, complemented
85C3×#888C2×C311yescharacteristic, complemented
86C3×#872—31no—
87C3×#872—31no—
88C3×#870—31no—
89C3×#869—31no—
90#63895C2×C311yescharacteristic
91#63888C2×C311yescharacteristic
92#63883C2×C311yescharacteristic
93#63871C2×C311yescharacteristic
94#63867C2×C311yescharacteristic, complemented
95#63866C2×C311yescharacteristic, complemented
96#63846C2×C311yescharacteristic, complemented
97#63846C2×C311yescharacteristic, complemented
98#63840C2×C311yescharacteristic, complemented
99#63839C2×C311yescharacteristic, complemented
100#63836C2×C311yescharacteristic
101#63836C2×C311yescharacteristic
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4×C3⋊D3—41no—
110C3×#634—41no—
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C32×Dic6—41no—
120C32×Dic6—41no—
121C3×#627—41no—
122C3×#624—41no—
123C3×#624Q814yescomplemented
124C3×#544—91no—
125#5729—31no—
126#5689—31no—
127C2×C32×Q8—31no—
128C2×C32×Q8—31no—
129C2×C4×C3⋊D3C22×C311yescharacteristic
130C2×#634C22×C311yescharacteristic
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—61no—
138C2×C3×Dic6—21no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×C3×Dic6—31no—
144C2×C3×Dic6—61no—
145C2×C3×Dic6C2×D311yescharacteristic
146C2×C3×Dic6C2×D311yescharacteristic
147C2×C3×Dic6C22×C311yescharacteristic
148C2×C3×Dic6C22×C311yescharacteristic
149C2×#627C22×C311yescharacteristic
150C2×#624C22×C311yescharacteristic
151C2×#624C22×C311yescharacteristic
152C32×C4⋊C4—21no—
153C32×C4⋊C4—21no—
154C32×C4⋊C4—21no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4—31no—
162C32×C4⋊C4—31no—
163C32×C4⋊C4—41no—
164C32×C4⋊C4C2×D311yescharacteristic
165C32×C4⋊C4C2×D311yescharacteristic
166C32×C4⋊C4C22×C311yescharacteristic
167C32×C42—31no—
168C32×C42—31no—
169#3752C22×C311yescharacteristic
170#3752C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172#3750C22×C311yescharacteristic
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—61no—
182C3×(C2×D3)⋊C4—61no—
183C3×C4⋊Dic3—21no—
184C3×C4⋊Dic3—21no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3C2×D311yescharacteristic
194C3×C4⋊Dic3C2×D311yescharacteristic
195C3×C4⋊Dic3C22×C311yescharacteristic
196C3×C4⋊Dic3C22×C311yescharacteristic
197C3×Dic3⋊C4—21no—
198C3×Dic3⋊C4—21no—
199C3×Dic3⋊C4—21no—
200C3×Dic3⋊C4—21no—
201C3×Dic3⋊C4—21no—
202C3×Dic3⋊C4—21no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—61no—
218C3×Dic3⋊C4—61no—
219C3×Dic3⋊C4C2×D311yescharacteristic
220C3×Dic3⋊C4C2×D311yescharacteristic
221C3×Dic3⋊C4C2×D311yescharacteristic
222C3×Dic3⋊C4C2×D311yescharacteristic
223C3×Dic3⋊C4C2×D311yescharacteristic
224C3×Dic3⋊C4C2×D311yescharacteristic
225C3×Dic3⋊C4C22×C311yescharacteristic
226C3×Dic3⋊C4C22×C311yescharacteristic
227C3×Dic3⋊C4C22×C311yescharacteristic
228C3×Dic3⋊C4C22×C311yescharacteristic
229C3×Dic3⋊C4C22×C311yescharacteristic
230C3×Dic3⋊C4C22×C311yescharacteristic
231C3×C4×Dic3—21no—
232C3×C4×Dic3—21no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236C3×C4×Dic3—31no—
237C3×C4×Dic3C2×D311yescharacteristic
238C3×C4×Dic3C2×D311yescharacteristic
239C3×C4×Dic3C22×C311yescharacteristic
240C3×C4×Dic3C22×C311yescharacteristic
241#3724C22×C311yescharacteristic
242Dic3⋊Dic3C22×C311yescharacteristic
243Dic3⋊Dic3C22×C311yescharacteristic
244Dic3⋊Dic3C22×C311yescharacteristic
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248Dic3⋊Dic3C22×C311yescharacteristic
249Dic3⋊Dic3C22×C311yescharacteristic
250#3722C22×C311yescharacteristic
251#3722C22×C311yescharacteristic
252Dic32C22×C311yescharacteristic
253Dic32C22×C311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3C2×Q812yes—
258C33×C4—21no—
259C33×C4—21no—
260C33×C4—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C32×Dic3—21no—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3C2×Q812yes—
271C32×Dic3C2×Q812yes—
272C3×C4⋊Q8—31no—
273C3×C4⋊Q8—31no—
274C3×C4⋊Q8—61no—
275C3×C4⋊Q8—91no—
276C3×C4⋊Q8—91no—
277C3×C4⋊Q8—91no—
278C3×#125—31no—
279C3×#125—31no—
280C3×#125—61no—
281C3×#125—91no—
282C3×#125—91no—
283C3×#125—91no—
284C3×C22⋊Q8—91no—
285C3×C22⋊Q8—91no—
286C3×C22⋊Q8—91no—
287C3×C22⋊Q8—91no—
288C3×#117—91no—
289C3×#117—91no—
290C2×C3×C4⋊C4—91no—
291#946—31no—
292#946—31no—
293#944—31no—
294#944—31no—
295#897—31no—
296#897—31no—
297#896—31no—
298#896—31no—
299#896—31no—
300#896—31no—
301#896—61no—
302#892—31no—
303#892—31no—
304D3×C4⋊C4—31no—
305D3×C4⋊C4—31no—
306#890—31no—
307#890—31no—
308#889—31no—
309#889—31no—
310#889—31no—
311#889C3×D311yescharacteristic, complemented
312#888—31no—
313#888—31no—
314#888—31no—
315#888C3×D311yescharacteristic, complemented
316#872—31no—
317#872—31no—
318#870—31no—
319#869—31no—
320C22×C3⋊D3C23×C311yescharacteristic
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—61no—
324C32×Q8—121no—
325C32×Q8—121no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—41no—
344C2×C32×C4—41no—
345C2×C32×C4—41no—
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348C2×C32×C4C22×D311yescharacteristic
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C23×C311yescharacteristic
353C2×C32×C4C23×C311yescharacteristic
354C2×C32×C4C23×C311yescharacteristic
355C2×C3⋊Dic3C23×C311yescharacteristic
356C2×C3⋊Dic3C23×C311yescharacteristic
357C2×C3⋊Dic3C23×C311yescharacteristic
358C4×C3⋊D3—41no—
359#634—41no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—21no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—61no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3C22×D311yescharacteristic
378C2×C3×Dic3C22×D311yescharacteristic
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C23×C311yescharacteristic
386C2×C3×Dic3C23×C311yescharacteristic
387C2×C3×Dic3C23×C311yescharacteristic
388C2×C3×Dic3C23×C311yescharacteristic
389C2×C3×Dic3C23×C311yescharacteristic
390C2×C3×Dic3C23×C311yescharacteristic
391C2×C3×Dic3C23×C311yescharacteristic
392C2×C3×Dic3C23×C311yescharacteristic
393C3×C4×D3—34no—
394C3×C4×D3—34no—
395C3×C4×D3—121no—
396C3×C4×D3—121no—
397C3×C4×D3—121no—
398C3×C4×D3—121no—
399C3×C4×D3—122no—
400C3×Dic6—41no—
401C3×Dic6—41no—
402C3×Dic6—41no—
403C3×Dic6—41no—
404C3×Dic6—42no—
405C3×Dic6—42no—
406C3×Dic6—121no—
407C3×Dic6—121no—
408C3×Dic6—121no—
409C3×Dic6—121no—
410C3×Dic6—122no—
411#627—41no—
412#624—41no—
413#624C3×Q814yescomplemented
414#544—91noSylow
415C2×C33C22×Q811yescharacteristic
416C2×C33H(5,𝔽2)11yescharacteristic
417C2×C332−1+411yescharacteristic
418C3×C3⋊D3—22no—
419C2×C3×Q8—31no—
420C2×C3×Q8—31no—
421C2×C3×Q8—31no—
422C2×C3×Q8—31no—
423C2×C3×Q8—61no—
424C2×C3×Q8—61no—
425C2×C3×Q8—91no—
426C2×C3×Q8—91no—
427C22×C3×C4—91no—
428C22×C3×C4—91no—
429C22×C3×C4—91no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—61no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—31no—
441C2×Dic6—61no—
442C2×Dic6C2×C3×D311yescharacteristic
443C2×Dic6C2×C3×D311yescharacteristic
444C3×C4⋊C4—21no—
445C3×C4⋊C4—21no—
446C3×C4⋊C4—21no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—31no—
449C3×C4⋊C4—31no—
450C3×C4⋊C4—31no—
451C3×C4⋊C4—31no—
452C3×C4⋊C4—31no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—31no—
462C3×C4⋊C4—31no—
463C3×C4⋊C4—41no—
464C3×C4⋊C4—61no—
465C3×C4⋊C4—61no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4—61no—
470C3×C4⋊C4—61no—
471C3×C4⋊C4—61no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C4⋊C4—91no—
478C3×C4⋊C4—91no—
479C3×C4⋊C4—91no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4D3211yescharacteristic
484C3×C4⋊C4C2×C3×D311yescharacteristic
485C3×C4⋊C4C2×C3×D311yescharacteristic
486C3×C22⋊C4—91no—
487C3×C22⋊C4—91no—
488C3×C22⋊C4—91no—
489C3×C22⋊C4—91no—
490C3×C42—31no—
491C3×C42—31no—
492C3×C42—31no—
493C3×C42—31no—
494C3×C42—61no—
495C3×C42—61no—
496C3×C42—91no—
497C3×C42—91no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—61no—
507(C2×D3)⋊C4—61no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—31no—
511C4⋊Dic3—31no—
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3C2×C3×D311yescharacteristic
517C4⋊Dic3C2×C3×D311yescharacteristic
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—61no—
533Dic3⋊C4—61no—
534Dic3⋊C4C2×C3×D311yescharacteristic
535Dic3⋊C4C2×C3×D311yescharacteristic
536Dic3⋊C4C2×C3×D311yescharacteristic
537Dic3⋊C4C2×C3×D311yescharacteristic
538Dic3⋊C4C2×C3×D311yescharacteristic
539Dic3⋊C4C2×C3×D311yescharacteristic
540C4×Dic3—31no—
541C4×Dic3—31no—
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3C2×C3×D311yescharacteristic
545C4×Dic3C2×C3×D311yescharacteristic
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—41no—
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C22×C32C24×C311yescharacteristic
553C2×C3⋊D3—21no—
554C2×C3⋊D3—21no—
555C2×C3⋊D3C2×C3×Q812yes—
556C2×C3×D3—32no—
557C2×C3×D3—32no—
558C2×C3×D3—62no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—61no—
563C2×C3×D3—121no—
564C2×C3×D3—121no—
565C32×C4—21no—
566C32×C4—22no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—21no—
575C32×C4—32no—
576C32×C4—32no—
577C32×C4—41no—
578C32×C4—41no—
579C32×C4—42no—
580C32×C4—41no—
581C32×C4—41no—
582C32×C4—41no—
583C32×C4—41no—
584C32×C4—41no—
585C32×C4—41no—
586C32×C4—61no—
587C32×C4—61no—
588C32×C4—61no—
589C32×C4—61no—
590C32×C4—61no—
591C32×C4—61no—
592C32×C4—81no—
593C32×C4—81no—
594C3⋊Dic3—21no—
595C3⋊Dic3—21no—
596C3⋊Dic3—21no—
597C3×Dic3—22no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—21no—
606C3×Dic3—21no—
607C3×Dic3—21no—
608C3×Dic3—21no—
609C3×Dic3—21no—
610C3×Dic3—22no—
611C3×Dic3—22no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—41no—
615C3×Dic3—41no—
616C3×Dic3—41no—
617C3×Dic3—62no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—121no—
625C3×Dic3—121no—
626C3×Dic3D3×Q812yes—
627C3×Dic3D3×Q812yes—
628C3×Dic3C2×C3×Q812yes—
629C3×Dic3C2×C3×Q812yes—
630C4⋊Q8—31no—
631C4⋊Q8—91no—
632C4⋊Q8—91no—
633C4⋊Q8—91no—
634#125—31no—
635#125—91no—
636#125—91no—
637#125—91no—
638C22⋊Q8—91no—
639C22⋊Q8—91no—
640C22⋊Q8—91no—
641C22⋊Q8—91no—
642#117—91no—
643#117—91no—
644C2×C4⋊C4—91no—
645C33#54411yescharacteristic, complemented, Sylow
646C23×C3—91no—
647C22×D3—31no—
648C22×D3—31no—
649C22×D3—61no—
650C3×Q8—121no—
651C3×Q8—121no—
652C3×Q8—121no—
653C3×Q8—121no—
654C3×Q8—122no—
655C3×Q8—122no—
656C3×Q8—361no—
657C3×Q8—361no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—31no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—41no—
684C2×C3×C4—41no—
685C2×C3×C4—41no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—94no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—91no—
698C2×C3×C4—361no—
699C2×C3×C4—361no—
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C2×D3211yescharacteristic
703C2×C3×C4C22×C3×D311yescharacteristic
704C2×C3×C4C22×C3×D311yescharacteristic
705C2×C3×C4C22×C3×D311yescharacteristic
706C2×C3×C4C22×C3×D311yescharacteristic
707C2×C3×C4C22×C3×D311yescharacteristic
708C2×C3×C4C22×C3×D311yescharacteristic
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3C22×C3×D311yescharacteristic
719C2×Dic3C22×C3×D311yescharacteristic
720C2×Dic3C22×C3×D311yescharacteristic
721C2×Dic3C22×C3×D311yescharacteristic
722C2×Dic3C22×C3×D311yescharacteristic
723C2×Dic3C22×C3×D311yescharacteristic
724C2×Dic3C22×C3×D311yescharacteristic
725C2×Dic3C22×C3×D311yescharacteristic
726C4×D3—34no—
727C4×D3—34no—
728C4×D3—121no—
729C4×D3—121no—
730C4×D3—121no—
731C4×D3—121no—
732C4×D3—122no—
733Dic6—41no—
734Dic6—41no—
735Dic6—121no—
736Dic6—121no—
737Dic6—121no—
738Dic6—121no—
739Dic6—122no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—21no—
748C2×C32—21no—
749C2×C32—41no—
750C2×C32—41no—
751C2×C32—41no—
752C2×C32#100411yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32#100711yescharacteristic
756C2×C32#100911yescharacteristic
757C2×C32#101011yescharacteristic
758C2×C32C22×C3×Q811yescharacteristic
759C2×C32C3×H(5,𝔽2)11yescharacteristic
760C2×C32C3×2−1+411yescharacteristic
761C3⋊D3—22no—
762C3×D3—62no—
763C3×D3—62no—
764C3×D3—122no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8—91no—
768C2×Q8—91no—
769C22×C4—91no—
770C22×C4—91no—
771C22×C4—91no—
772C4⋊C4—31no—
773C4⋊C4—31no—
774C4⋊C4—31no—
775C4⋊C4—31no—
776C4⋊C4—31no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4—91no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4C3×D3211yescharacteristic
792C22⋊C4—91no—
793C22⋊C4—91no—
794C22⋊C4—91no—
795C22⋊C4—91no—
796C42—31no—
797C42—31no—
798C42—91no—
799C42—91no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—21no—
803C22×C3—41no—
804C22×C3—92no—
805C22×C3—181no—
806C22×C3—181no—
807C22×C3C22×D3211yescharacteristic
808C22×C3C23×C3×D311yescharacteristic
809C22×C3C23×C3×D311yescharacteristic
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—121no—
818C2×D3—121no—
819C3×C4—22no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—32no—
830C3×C4—32no—
831C3×C4—32no—
832C3×C4—32no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—41no—
838C3×C4—41no—
839C3×C4—41no—
840C3×C4—41no—
841C3×C4—42no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—62no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—61no—
854C3×C4—61no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—81no—
858C3×C4—81no—
859C3×C4—121no—
860C3×C4—121no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—121no—
864C3×C4—181no—
865C3×C4—181no—
866C3×C4—181no—
867Dic3—21no—
868Dic3—21no—
869Dic3—21no—
870Dic3—21no—
871Dic3—21no—
872Dic3—21no—
873Dic3—62no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—61no—
880Dic3—121no—
881Dic3—121no—
882Dic3C3×D3×Q812yes—
883Dic3C3×D3×Q812yes—
884C32—21no—
885C32—21no—
886C32—21no—
887C32—41no—
888C32#568911yescharacteristic, complemented
889C32#572911yescharacteristic, complemented
890C32C3×#54411yescharacteristic, complemented
891C23—91no—
892Q8—121no—
893Q8—121no—
894Q8—361no—
895Q8—361no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—31no—
901C2×C4—31no—
902C2×C4—31no—
903C2×C4—31no—
904C2×C4—94no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—361no—
909C2×C4—361no—
910C2×C4C2×C3×D3211yescharacteristic
911C2×C4C2×C3×D3211yescharacteristic
912C2×C4C2×C3×D3211yescharacteristic
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—182no—
926C2×C3#6429711yescharacteristic
927C2×C3#6431411yescharacteristic
928C2×C3D32×Q811yescharacteristic
929C2×C3C3×#100411yescharacteristic
930C2×C3C2×C3×D3×Q811yescharacteristic
931C2×C3C2×C3×D3×Q811yescharacteristic
932C2×C3C3×#100711yescharacteristic
933C2×C3C3×#100911yescharacteristic
934C2×C3C3×#101011yescharacteristic
935D3—62no—
936D3—62no—
937D3—122no—
938C22—92no—
939C22—181no—
940C22—181no—
941C22C22×C3×D3211yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—32no—
946C4—32no—
947C4—61no—
948C4—61no—
949C4—61no—
950C4—61no—
951C4—61no—
952C4—61no—
953C4—181no—
954C4—181no—
955C4—181no—
956C3—21no—
957C3—21no—
958C3—21no—
959C3—41no—
960C3#1059440011yescharacteristic, direct product factor
961C3C3×#568911yescharacteristic, complemented
962C3C3×#572911yescharacteristic, complemented
963C2—182no—
964C2C3×#6429711yescharacteristic
965C2C3×#6431411yescharacteristic
966C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C3×C3⋊D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×#889C2semidirect
3. C32×#888C2semidirect
8. C3×#63867C2semidirect
9. C3×#63866C2semidirect
10. C3×#63846C2semidirect
11. C3×#63846C2semidirect
12. C3×#63840C2semidirect
13. C3×#63839C2semidirect
18. #10594400C3direct (N × H)
78. C3×#889D3semidirect
79. C3×#889C2×C3semidirect
84. C3×#888D3semidirect
85. C3×#888C2×C3semidirect
94. #63867C2×C3semidirect
95. #63866C2×C3semidirect
96. #63846C2×C3semidirect
97. #63846C2×C3semidirect
98. #63840C2×C3semidirect
99. #63839C2×C3semidirect
123. C3×#624Q8semidirect
311. #889C3×D3semidirect
315. #888C3×D3semidirect
413. #624C3×Q8semidirect
645. C33#544semidirect
888. C32#5689semidirect
889. C32#5729semidirect
890. C32C3×#544semidirect
960. C3#10594400direct (N × H)
961. C3C3×#5689semidirect
962. C3C3×#5729semidirect

Maximal subgroups

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

subgroupindex
C3×#641052
C32×#8892
C32×#8882
C3×#638952
C3×#638882
C3×#638832
C3×#638712
C3×#638672
C3×#638662
C3×#638462
C3×#638402
C3×#638392
C3×#638362
C3×#57293
C3×#56893
#105944003