Finite Group Databasebeta

← C3×#10594328 #13173935

Subgroups — C3×#10594328 #13173935

Order 1728.

1326 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3799C211yesmaximal, characteristic
2C2×C3×#3797C211yesmaximal, characteristic, complemented
3C3×#64103C211yesmaximal, characteristic, complemented
4C32×#896C211yesmaximal, characteristic, complemented
5C32×#888C211yesmaximal, characteristic, complemented
6C3×#63907C211yesmaximal, characteristic, complemented
7C3×#63897C211yesmaximal, characteristic, complemented
8C3×#63895C211yesmaximal, characteristic, complemented
9C3×#63888C211yesmaximal, characteristic, complemented
10C3×#63854C211yesmaximal, characteristic, complemented
11C3×#63853C211yesmaximal, characteristic, complemented
12C3×#63852C211yesmaximal, characteristic, complemented
13C3×#63851C211yesmaximal, characteristic, complemented
14C3×#63839C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5724—31nomaximal
17C3×#5628—31nomaximal
18#10594328C311yesmaximal, characteristic, direct product factor
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic
32C3×#3799—24no—
33C3×#3797—24no—
34C33×C4⋊C4C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×C4×Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C2×C3×#239—31no—
57C2×C3×D3×Q8—31no—
58C2×C3×D3×Q8—31no—
59C2×C3×#235—31no—
60C2×#3799C2×C311yescharacteristic
61C2×#3797C2×C311yescharacteristic, complemented
62C32×C4⋊Q8—31no—
63C32×C22⋊Q8—31no—
64#64103C2×C311yescharacteristic, complemented
65C3×#947—31no—
66C3×#946—31no—
67C3×#944—31no—
68C3×#924—31no—
69C3×#897—31no—
70C3×#896—21no—
71C3×#896—31no—
72C3×#896—31no—
73C3×#896—31no—
74C3×#896D311yescharacteristic, complemented
75C3×#896C2×C311yescharacteristic, complemented
76C3×#894—31no—
77C3×#894—31no—
78C3×#894—31no—
79C3×#894—31no—
80C3×#894—31no—
81C3×#894—31no—
82C3×#894—61no—
83C3×#892—31no—
84C3×#888—21no—
85C3×#888—31no—
86C3×#888D311yescharacteristic, complemented
87C3×#888C2×C311yescharacteristic, complemented
88C3×#885—31no—
89C3×#885—31no—
90C3×#883—31no—
91C3×#883—31no—
92C3×#875—31no—
93C3×#872—31no—
94#63907C2×C311yescharacteristic, complemented
95#63897C2×C311yescharacteristic, complemented
96#63895C2×C311yescharacteristic, complemented
97#63888C2×C311yescharacteristic, complemented
98#63854C2×C311yescharacteristic, complemented
99#63853C2×C311yescharacteristic, complemented
100#63852C2×C311yescharacteristic, complemented
101#63851C2×C311yescharacteristic, complemented
102#63839C2×C311yescharacteristic, complemented
103#63836C2×C311yescharacteristic, complemented
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C33×C4C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—22no—
113C3×C4×C3⋊D3—22no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×C4×D3—22no—
122C32×Dic6—22no—
123C32×Dic6—22no—
124C32×Dic6—22no—
125C3×#627—22no—
126C3×#627—22no—
127C3×#626—22no—
128C3×#626—22no—
129C3×#624—22no—
130C3×#624—22no—
131C3×#624D414yes—
132C3×#536—91no—
133#5724—31no—
134#5628—31no—
135C2×C32×Q8—31no—
136C2×C32×Q8—31no—
137C2×C32×Q8—31no—
138C22×C32×C4—31no—
139C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
140C2×C4×C3⋊D3C22×C311yescharacteristic
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C3×#239—64no—
144C3×D3×Q8—64no—
145C3×D3×Q8—64no—
146C3×#235—64no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—31no—
151C2×C3×D12—61no—
152C2×C3×C4×D3—21no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—61no—
162C2×C3×C4×D3C2×D311yescharacteristic
163C2×C3×C4×D3C22×C311yescharacteristic
164C2×C3×Dic6—21no—
165C2×C3×Dic6—21no—
166C2×C3×Dic6—21no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×C3×Dic6C2×D311yescharacteristic
172C2×C3×Dic6C2×D311yescharacteristic
173C2×C3×Dic6C2×D311yescharacteristic
174C2×C3×Dic6C22×C311yescharacteristic
175C2×C3×Dic6C22×C311yescharacteristic
176C2×C3×Dic6C22×C311yescharacteristic
177C2×#627C22×C311yescharacteristic
178C2×#627C22×C311yescharacteristic
179C2×#626C22×C311yescharacteristic
180C2×#626C22×C311yescharacteristic
181C2×#624C22×C311yescharacteristic
182C2×#624C22×C311yescharacteristic
183C2×#624C22×C311yescharacteristic
184#3799—24no—
185#3797—24no—
186C32×C4⋊C4—21no—
187C32×C4⋊C4—21no—
188C32×C4⋊C4—21no—
189C32×C4⋊C4—31no—
190C32×C4⋊C4—31no—
191C32×C4⋊C4—31no—
192C32×C4⋊C4—31no—
193C32×C4⋊C4—31no—
194C32×C4⋊C4—41no—
195C32×C4⋊C4C2×D311yescharacteristic
196C32×C4⋊C4C2×D311yescharacteristic
197C32×C4⋊C4C22×C311yescharacteristic
198C32×C22⋊C4—31no—
199C32×C22⋊C4—31no—
200C32×C42—31no—
201#3752C22×C311yescharacteristic
202#3752C22×C311yescharacteristic
203#3752C22×C311yescharacteristic
204#3750C22×C311yescharacteristic
205C3×#217—31no—
206C3×#217—31no—
207C3×(C2×D3)⋊C4—21no—
208C3×(C2×D3)⋊C4—21no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—61no—
224C3×(C2×D3)⋊C4—61no—
225C3×(C2×D3)⋊C4—61no—
226C3×(C2×D3)⋊C4C2×D311yescharacteristic
227C3×(C2×D3)⋊C4C2×D311yescharacteristic
228C3×(C2×D3)⋊C4C22×C311yescharacteristic
229C3×(C2×D3)⋊C4C22×C311yescharacteristic
230C3×C4⋊Dic3—21no—
231C3×C4⋊Dic3—31no—
232C3×C4⋊Dic3—31no—
233C3×C4⋊Dic3C2×D311yescharacteristic
234C3×C4⋊Dic3C22×C311yescharacteristic
235C3×Dic3⋊C4—21no—
236C3×Dic3⋊C4—21no—
237C3×Dic3⋊C4—21no—
238C3×Dic3⋊C4—21no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—61no—
246C3×Dic3⋊C4C2×D311yescharacteristic
247C3×Dic3⋊C4C2×D311yescharacteristic
248C3×Dic3⋊C4C2×D311yescharacteristic
249C3×Dic3⋊C4C2×D311yescharacteristic
250C3×Dic3⋊C4C22×C311yescharacteristic
251C3×Dic3⋊C4C22×C311yescharacteristic
252C3×Dic3⋊C4C22×C311yescharacteristic
253C3×Dic3⋊C4C22×C311yescharacteristic
254C3×C4×Dic3—21no—
255C3×C4×Dic3—31no—
256C3×C4×Dic3—31no—
257C3×C4×Dic3C2×D311yescharacteristic
258C3×C4×Dic3C22×C311yescharacteristic
259#3724C22×C311yescharacteristic
260Dic3⋊Dic3C22×C311yescharacteristic
261Dic3⋊Dic3C22×C311yescharacteristic
262#3722C22×C311yescharacteristic
263#3722C22×C311yescharacteristic
264#3722C22×C311yescharacteristic
265(C2×D3)⋊Dic3C22×C311yescharacteristic
266(C2×D3)⋊Dic3C22×C311yescharacteristic
267Dic32C22×C311yescharacteristic
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3C2×D412yes—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C33×C4—21no—
279C33×C4—21no—
280C33×C4—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3C2×D412yes—
289C32×Dic3C2×D412yes—
290C2×C3×#41—91no—
291C22×C3×Q8—91no—
292C2×#239—31no—
293C2×D3×Q8—31no—
294C2×D3×Q8—31no—
295C2×#235—31no—
296C3×C4⋊Q8—31no—
297C3×C4⋊Q8—31no—
298C3×C4⋊Q8—61no—
299C3×C4⋊Q8—91no—
300C3×#124—91no—
301C3×#124—91no—
302C3×#123—91no—
303C3×#123—91no—
304C3×#123—91no—
305C3×#123—91no—
306C3×C22⋊Q8—31no—
307C3×C22⋊Q8—31no—
308C3×C22⋊Q8—61no—
309C3×C22⋊Q8—91no—
310C3×C22⋊Q8—91no—
311C3×C22⋊Q8—91no—
312C3×#117—91no—
313#947—31no—
314#946—31no—
315#944—31no—
316#924—31no—
317#897—31no—
318#896—31no—
319#896—31no—
320#896—31no—
321#896C3×D311yescharacteristic, complemented
322#894—31no—
323#894—31no—
324#894—31no—
325#894—31no—
326#894—31no—
327#894—31no—
328#894—61no—
329#892—31no—
330#888—31no—
331#888C3×D311yescharacteristic, complemented
332#885—31no—
333#885—31no—
334#883—31no—
335#883—31no—
336#875—31no—
337#872—31no—
338C23×C32—31no—
339C22×C3⋊D3C23×C311yescharacteristic
340C22×C3⋊D3C23×C311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3—61no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C23×C311yescharacteristic
350C32×Q8—62no—
351C32×Q8—62no—
352C32×Q8—62no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—41no—
370C2×C32×C4—41no—
371C2×C32×C4—41no—
372C2×C32×C4—62no—
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C23×C311yescharacteristic
380C2×C32×C4C23×C311yescharacteristic
381C2×C32×C4C23×C311yescharacteristic
382C2×C3⋊Dic3C23×C311yescharacteristic
383C2×C3⋊Dic3C23×C311yescharacteristic
384C4⋊(C3⋊D3)—22no—
385C4×C3⋊D3—22no—
386C3×#67—62no—
387C3×#67—62no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C23×C311yescharacteristic
409C2×C3×Dic3C23×C311yescharacteristic
410C2×C3×Dic3C23×C311yescharacteristic
411C2×C3×Dic3C23×C311yescharacteristic
412C2×C3×Dic3C23×C311yescharacteristic
413C2×C3×Dic3C23×C311yescharacteristic
414C2×C3×Dic3C23×C311yescharacteristic
415C3×D12—62no—
416C3×D12—62no—
417C3×D12—62no—
418C3×D12—62no—
419C3×D12—122no—
420C3×C4×D3—22no—
421C3×C4×D3—22no—
422C3×C4×D3—34no—
423C3×C4×D3—34no—
424C3×C4×D3—42no—
425C3×C4×D3—62no—
426C3×C4×D3—62no—
427C3×C4×D3—62no—
428C3×C4×D3—62no—
429C3×C4×D3—62no—
430C3×C4×D3—62no—
431C3×C4×D3—122no—
432C3×Dic6—22no—
433C3×Dic6—22no—
434C3×Dic6—22no—
435C3×Dic6—22no—
436C3×Dic6—22no—
437C3×Dic6—22no—
438C3×Dic6—42no—
439C3×Dic6—42no—
440C3×Dic6—42no—
441C3×Dic6—62no—
442C3×Dic6—62no—
443C3×Dic6—62no—
444C3×Dic6—62no—
445#627—22no—
446#627—22no—
447#626—22no—
448#626—22no—
449#624—22no—
450#624—22no—
451#624C3×D414yes—
452#536—91noSylow
453C2×C33C22×D411yescharacteristic
454C2×C332−1+411yescharacteristic
455C2×C332−1+411yescharacteristic
456C3×C3⋊D3—22no—
457C3×C3⋊D3—41no—
458C32×D3—41no—
459C3×#41—184no—
460C2×C3×Q8—31no—
461C2×C3×Q8—31no—
462C2×C3×Q8—31no—
463C2×C3×Q8—31no—
464C2×C3×Q8—31no—
465C2×C3×Q8—31no—
466C2×C3×Q8—61no—
467C2×C3×Q8—61no—
468C2×C3×Q8—61no—
469C2×C3×Q8—91no—
470C2×C3×Q8—91no—
471C2×C3×Q8—184no—
472C2×C3×D4—91no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C22×C3×C4—31no—
476C22×C3×C4—31no—
477C22×C3×C4—61no—
478C22×C3×C4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484#239—64no—
485D3×Q8—64no—
486D3×Q8—64no—
487#235—64no—
488C2×D12—31no—
489C2×D12—31no—
490C2×D12—31no—
491C2×D12—31no—
492C2×D12—61no—
493C2×C4×D3—31no—
494C2×C4×D3—31no—
495C2×C4×D3—31no—
496C2×C4×D3—31no—
497C2×C4×D3—31no—
498C2×C4×D3—31no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—61no—
502C2×C4×D3C2×C3×D311yescharacteristic
503C2×Dic6—31no—
504C2×Dic6—31no—
505C2×Dic6—31no—
506C2×Dic6—31no—
507C2×Dic6C2×C3×D311yescharacteristic
508C2×Dic6C2×C3×D311yescharacteristic
509C2×Dic6C2×C3×D311yescharacteristic
510C3×C4⋊C4—21no—
511C3×C4⋊C4—21no—
512C3×C4⋊C4—21no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—31no—
515C3×C4⋊C4—31no—
516C3×C4⋊C4—31no—
517C3×C4⋊C4—31no—
518C3×C4⋊C4—31no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4—31no—
521C3×C4⋊C4—31no—
522C3×C4⋊C4—31no—
523C3×C4⋊C4—41no—
524C3×C4⋊C4—61no—
525C3×C4⋊C4—61no—
526C3×C4⋊C4—61no—
527C3×C4⋊C4—61no—
528C3×C4⋊C4—61no—
529C3×C4⋊C4—91no—
530C3×C4⋊C4—91no—
531C3×C4⋊C4—91no—
532C3×C4⋊C4—91no—
533C3×C4⋊C4D3211yescharacteristic
534C3×C4⋊C4C2×C3×D311yescharacteristic
535C3×C4⋊C4C2×C3×D311yescharacteristic
536C3×C22⋊C4—31no—
537C3×C22⋊C4—31no—
538C3×C22⋊C4—31no—
539C3×C22⋊C4—31no—
540C3×C22⋊C4—61no—
541C3×C22⋊C4—61no—
542C3×C22⋊C4—91no—
543C3×C22⋊C4—91no—
544C3×C22⋊C4—91no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550C3×C42—31no—
551C3×C42—31no—
552C3×C42—61no—
553C3×C42—91no—
554#217—31no—
555#217—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—31no—
563(C2×D3)⋊C4—31no—
564(C2×D3)⋊C4—31no—
565(C2×D3)⋊C4—31no—
566(C2×D3)⋊C4—31no—
567(C2×D3)⋊C4—31no—
568(C2×D3)⋊C4—31no—
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—61no—
571(C2×D3)⋊C4—61no—
572(C2×D3)⋊C4—61no—
573(C2×D3)⋊C4C2×C3×D311yescharacteristic
574(C2×D3)⋊C4C2×C3×D311yescharacteristic
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3C2×C3×D311yescharacteristic
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—61no—
585Dic3⋊C4C2×C3×D311yescharacteristic
586Dic3⋊C4C2×C3×D311yescharacteristic
587Dic3⋊C4C2×C3×D311yescharacteristic
588Dic3⋊C4C2×C3×D311yescharacteristic
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3C2×C3×D311yescharacteristic
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—41no—
596C22×C32—61no—
597C22×C32—61no—
598C22×C32—61no—
599C22×C32C23×D311yescharacteristic
600C22×C32C23×D311yescharacteristic
601C22×C32C24×C311yescharacteristic
602C2×C3⋊D3—21no—
603C2×C3⋊D3—21no—
604C2×C3⋊D3—21no—
605C2×C3⋊D3—21no—
606C2×C3⋊D3—21no—
607C2×C3⋊D3C2×C3×D412yes—
608C2×C3×D3—22no—
609C2×C3×D3—21no—
610C2×C3×D3—21no—
611C2×C3×D3—21no—
612C2×C3×D3—21no—
613C2×C3×D3—21no—
614C2×C3×D3—21no—
615C2×C3×D3—32no—
616C2×C3×D3—32no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—62no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—121no—
631C2×C3×D3—121no—
632C2×C3×D3—121no—
633C2×C3×D3—121no—
634C2×C3×D3—121no—
635C32×C4—21no—
636C32×C4—22no—
637C32×C4—21no—
638C32×C4—21no—
639C32×C4—21no—
640C32×C4—21no—
641C32×C4—21no—
642C32×C4—21no—
643C32×C4—21no—
644C32×C4—21no—
645C32×C4—32no—
646C32×C4—32no—
647C32×C4—41no—
648C32×C4—41no—
649C32×C4—42no—
650C32×C4—41no—
651C32×C4—41no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—41no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C32×C4—81no—
662C32×C4—81no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3×Dic3—22no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—22no—
677C3×Dic3—22no—
678C3×Dic3—41no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3D3×D412yes—
689C3×Dic3D3×D412yes—
690C3×Dic3C2×C3×D412yes—
691C3×Dic3C2×C3×D412yes—
692C2×#41—91no—
693C22×Q8—91no—
694C4⋊Q8—31no—
695C4⋊Q8—91no—
696#124—91no—
697#124—91no—
698#123—91no—
699#123—91no—
700#123—91no—
701#123—91no—
702C22⋊Q8—31no—
703C22⋊Q8—91no—
704C22⋊Q8—91no—
705C22⋊Q8—91no—
706#117—91no—
707C33#53611yescharacteristic, complemented, Sylow
708C23×C3—31no—
709C23×C3—31no—
710C23×C3—61no—
711C23×C3—91no—
712C23×C3—91no—
713C22×D3—31no—
714C22×D3—31no—
715C22×D3—31no—
716C22×D3—31no—
717C22×D3—61no—
718C22×D3—61no—
719C22×D3C22×C3×D311yescharacteristic
720C3×Q8—62no—
721C3×Q8—62no—
722C3×Q8—62no—
723C3×Q8—62no—
724C3×Q8—62no—
725C3×Q8—62no—
726C3×Q8—122no—
727C3×Q8—122no—
728C3×Q8—122no—
729C3×Q8—182no—
730C3×Q8—182no—
731C3×D4—182no—
732C3×D4—182no—
733C3×D4—182no—
734C2×C3×C4—21no—
735C2×C3×C4—21no—
736C2×C3×C4—21no—
737C2×C3×C4—21no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—41no—
758C2×C3×C4—41no—
759C2×C3×C4—41no—
760C2×C3×C4—61no—
761C2×C3×C4—61no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—62no—
768C2×C3×C4—62no—
769C2×C3×C4—94no—
770C2×C3×C4—91no—
771C2×C3×C4—91no—
772C2×C3×C4—122no—
773C2×C3×C4—182no—
774C2×C3×C4—182no—
775C2×C3×C4—182no—
776C2×C3×C4C2×D3211yescharacteristic
777C2×C3×C4C2×D3211yescharacteristic
778C2×C3×C4C2×D3211yescharacteristic
779C2×C3×C4C22×C3×D311yescharacteristic
780C2×C3×C4C22×C3×D311yescharacteristic
781C2×C3×C4C22×C3×D311yescharacteristic
782C2×C3×C4C22×C3×D311yescharacteristic
783C2×C3×C4C22×C3×D311yescharacteristic
784C2×C3×C4C22×C3×D311yescharacteristic
785#67—62no—
786#67—62no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3C22×C3×D311yescharacteristic
794C2×Dic3C22×C3×D311yescharacteristic
795C2×Dic3C22×C3×D311yescharacteristic
796C2×Dic3C22×C3×D311yescharacteristic
797C2×Dic3C22×C3×D311yescharacteristic
798C2×Dic3C22×C3×D311yescharacteristic
799C2×Dic3C22×C3×D311yescharacteristic
800D12—62no—
801D12—62no—
802D12—62no—
803D12—62no—
804D12—122no—
805C4×D3—22no—
806C4×D3—34no—
807C4×D3—34no—
808C4×D3—62no—
809C4×D3—62no—
810C4×D3—62no—
811C4×D3—62no—
812C4×D3—62no—
813C4×D3—62no—
814C4×D3—122no—
815Dic6—22no—
816Dic6—22no—
817Dic6—22no—
818Dic6—62no—
819Dic6—62no—
820Dic6—62no—
821Dic6—62no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—41no—
832C2×C32—41no—
833C2×C32—41no—
834C2×C32—121no—
835C2×C32C2×D3×D411yescharacteristic
836C2×C32C2×D3×D411yescharacteristic
837C2×C32#100711yescharacteristic
838C2×C32#100711yescharacteristic
839C2×C32#100711yescharacteristic
840C2×C32#101011yescharacteristic
841C2×C32C22×C3×D411yescharacteristic
842C2×C32C3×2−1+411yescharacteristic
843C2×C32C3×2−1+411yescharacteristic
844C3⋊D3—22no—
845C3⋊D3—41no—
846C3×D3—42no—
847C3×D3—41no—
848C3×D3—41no—
849C3×D3—62no—
850C3×D3—62no—
851C3×D3—122no—
852C3×D3—121no—
853C3×D3—121no—
854C3×D3—241no—
855#41—184no—
856C2×Q8—31no—
857C2×Q8—31no—
858C2×Q8—31no—
859C2×Q8—91no—
860C2×Q8—91no—
861C2×Q8—184no—
862C2×D4—91no—
863C2×D4—91no—
864C2×D4—91no—
865C22×C4—31no—
866C22×C4—91no—
867C22×C4—91no—
868C22×C4—91no—
869C22×C4—91no—
870C4⋊C4—31no—
871C4⋊C4—31no—
872C4⋊C4—31no—
873C4⋊C4—31no—
874C4⋊C4—31no—
875C4⋊C4—91no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—91no—
879C4⋊C4C3×D3211yescharacteristic
880C22⋊C4—31no—
881C22⋊C4—31no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—91no—
889C22⋊C4—91no—
890C42—31no—
891C42—91no—
892C22×C3—21no—
893C22×C3—21no—
894C22×C3—21no—
895C22×C3—41no—
896C22×C3—62no—
897C22×C3—61no—
898C22×C3—61no—
899C22×C3—61no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—92no—
904C22×C3—121no—
905C22×C3—121no—
906C22×C3—181no—
907C22×C3—181no—
908C22×C3—181no—
909C22×C3—181no—
910C22×C3—181no—
911C22×C3C22×D3211yescharacteristic
912C22×C3C23×C3×D311yescharacteristic
913C22×C3C23×C3×D311yescharacteristic
914C2×D3—21no—
915C2×D3—21no—
916C2×D3—21no—
917C2×D3—32no—
918C2×D3—32no—
919C2×D3—62no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C3×C4—22no—
936C3×C4—21no—
937C3×C4—21no—
938C3×C4—21no—
939C3×C4—21no—
940C3×C4—21no—
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—32no—
946C3×C4—32no—
947C3×C4—32no—
948C3×C4—32no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—41no—
956C3×C4—41no—
957C3×C4—42no—
958C3×C4—62no—
959C3×C4—62no—
960C3×C4—62no—
961C3×C4—61no—
962C3×C4—61no—
963C3×C4—61no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—81no—
972C3×C4—81no—
973C3×C4—121no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—181no—
978C3×C4—181no—
979Dic3—21no—
980Dic3—21no—
981Dic3—21no—
982Dic3—21no—
983Dic3—21no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—121no—
989Dic3—121no—
990Dic3C3×D3×D412yes—
991Dic3C3×D3×D412yes—
992C32—21no—
993C32—21no—
994C32—21no—
995C32—41no—
996C32#562811yescharacteristic, complemented
997C32#572411yescharacteristic, complemented
998C32C3×#53611yescharacteristic, complemented
999C23—31no—
1000C23—91no—
1001C23—91no—
1002Q8—62no—
1003Q8—62no—
1004Q8—62no—
1005Q8—182no—
1006Q8—182no—
1007D4—182no—
1008D4—182no—
1009D4—182no—
1010C2×C4—31no—
1011C2×C4—31no—
1012C2×C4—31no—
1013C2×C4—31no—
1014C2×C4—31no—
1015C2×C4—31no—
1016C2×C4—31no—
1017C2×C4—62no—
1018C2×C4—94no—
1019C2×C4—91no—
1020C2×C4—91no—
1021C2×C4—182no—
1022C2×C4—182no—
1023C2×C4—182no—
1024C2×C4C2×C3×D3211yescharacteristic
1025C2×C4C2×C3×D3211yescharacteristic
1026C2×C4C2×C3×D3211yescharacteristic
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—41no—
1037C2×C3—41no—
1038C2×C3—41no—
1039C2×C3—122no—
1040C2×C3—121no—
1041C2×C3—121no—
1042C2×C3—182no—
1043C2×C3—361no—
1044C2×C3#6429711yescharacteristic
1045C2×C3D32×D411yescharacteristic
1046C2×C3#6431611yescharacteristic
1047C2×C3C2×C3×D3×D411yescharacteristic
1048C2×C3C2×C3×D3×D411yescharacteristic
1049C2×C3C3×#100711yescharacteristic
1050C2×C3C3×#100711yescharacteristic
1051C2×C3C3×#100711yescharacteristic
1052C2×C3C3×#101011yescharacteristic
1053D3—41no—
1054D3—62no—
1055D3—62no—
1056D3—122no—
1057D3—121no—
1058D3—121no—
1059D3—241no—
1060C22—61no—
1061C22—61no—
1062C22—61no—
1063C22—92no—
1064C22—181no—
1065C22—181no—
1066C22—181no—
1067C22—181no—
1068C22—181no—
1069C22C22×C3×D3211yescharacteristic
1070C4—21no—
1071C4—21no—
1072C4—21no—
1073C4—32no—
1074C4—32no—
1075C4—61no—
1076C4—61no—
1077C4—61no—
1078C4—61no—
1079C4—61no—
1080C4—181no—
1081C4—181no—
1082C3—21no—
1083C3—21no—
1084C3—21no—
1085C3—41no—
1086C3#1059432811yescharacteristic, direct product factor
1087C3C3×#562811yescharacteristic, complemented
1088C3C3×#572411yescharacteristic, complemented
1089C2—121no—
1090C2—182no—
1091C2—361no—
1092C2C3×#6429711yescharacteristic
1093C2C3×D32×D411yescharacteristic
1094C2C3×#6431611yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#3799C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#536
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. C2×C3×#3797C2semidirect
3. C3×#64103C2semidirect
4. C32×#896C2semidirect
5. C32×#888C2semidirect
6. C3×#63907C2semidirect
7. C3×#63897C2semidirect
8. C3×#63895C2semidirect
9. C3×#63888C2semidirect
10. C3×#63854C2semidirect
11. C3×#63853C2semidirect
12. C3×#63852C2semidirect
13. C3×#63851C2semidirect
14. C3×#63839C2semidirect
15. C3×#63836C2semidirect
18. #10594328C3direct (N × H)
61. C2×#3797C2×C3semidirect
64. #64103C2×C3semidirect
74. C3×#896D3semidirect
75. C3×#896C2×C3semidirect
86. C3×#888D3semidirect
87. C3×#888C2×C3semidirect
94. #63907C2×C3semidirect
95. #63897C2×C3semidirect
96. #63895C2×C3semidirect
97. #63888C2×C3semidirect
98. #63854C2×C3semidirect
99. #63853C2×C3semidirect
100. #63852C2×C3semidirect
101. #63851C2×C3semidirect
102. #63839C2×C3semidirect
103. #63836C2×C3semidirect
321. #896C3×D3semidirect
331. #888C3×D3semidirect
707. C33#536semidirect
996. C32#5628semidirect
997. C32#5724semidirect
998. C32C3×#536semidirect
1086. C3#10594328direct (N × H)
1087. C3C3×#5628semidirect
1088. C3C3×#5724semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37992
C2×C3×#37972
C3×#641032
C32×#8962
C32×#8882
C3×#639072
C3×#638972
C3×#638952
C3×#638882
C3×#638542
C3×#638532
C3×#638522
C3×#638512
C3×#638392
C3×#638362
C3×#57243
C3×#56283
#105943283