Finite Group Databasebeta

← C3×#10594386 #13173948

Subgroups — C3×#10594386 #13173948

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64098C211yesmaximal, characteristic, complemented
2C32×#896C211yesmaximal, characteristic
3C32×#887C211yesmaximal, characteristic, complemented
4C3×#63893C211yesmaximal, characteristic
5C3×#63887C211yesmaximal, characteristic
6C3×#63877C211yesmaximal, characteristic
7C3×#63877C211yesmaximal, characteristic
8C3×C4×D3×Dic3C211yesmaximal, characteristic
9C3×#63870C211yesmaximal, characteristic, complemented
10C3×#63851C211yesmaximal, characteristic
11C3×Dic3×Dic6C211yesmaximal, characteristic, complemented
12C3×#63839C211yesmaximal, characteristic, complemented
13C3×#63839C211yesmaximal, characteristic, complemented
14C3×#63837C211yesmaximal, characteristic, complemented
15C3×#63837C211yesmaximal, characteristic, complemented
16C3×#5622—31nomaximal
17C3×#5578—31nomaximal
18#10594386C311yesmaximal, characteristic, direct product factor
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C3×#3750C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×C4×C3⋊Dic3C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×C4×Dic3C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C32×C4×Dic3C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×C22⋊Q8—31no—
55C32×C4×Q8—31no—
56#64098C2×C311yescharacteristic, complemented
57C3×#946—31no—
58C3×Q8×Dic3—31no—
59C3×#944—31no—
60C3×#944—31no—
61C3×#924—31no—
62C2×C3×C4×Dic3—31no—
63C3×#897—31no—
64C3×#896—21no—
65C3×#896—31no—
66C3×#896D311yescharacteristic
67C3×#896C2×C311yescharacteristic
68C3×#889—31no—
69C3×#889—31no—
70C3×#889—31no—
71C3×#889—31no—
72C3×#889—61no—
73C3×#888—31no—
74C3×#888—31no—
75C3×#887—21no—
76C3×#887—31no—
77C3×#887—31no—
78C3×#887D311yescharacteristic, complemented
79C3×#887C2×C311yescharacteristic, complemented
80C3×#878—31no—
81C3×#878—31no—
82C3×#877—31no—
83C3×#877—31no—
84C3×#872—31no—
85C3×#872—31no—
86C3×C42×D3—31no—
87C3×C4×Dic6—31no—
88C3×C4×Dic6—31no—
89C3×C4×Dic6—31no—
90#63893C2×C311yescharacteristic
91#63887C2×C311yescharacteristic
92#63877C2×C311yescharacteristic
93#63877C2×C311yescharacteristic
94C4×D3×Dic3C2×C311yescharacteristic
95#63870C2×C311yescharacteristic, complemented
96#63851C2×C311yescharacteristic
97Dic3×Dic6C2×C311yescharacteristic, complemented
98#63839C2×C311yescharacteristic, complemented
99#63839C2×C311yescharacteristic, complemented
100#63837C2×C311yescharacteristic, complemented
101#63837C2×C311yescharacteristic, complemented
102C22×C32×D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118C32×Dic6—22no—
119C32×Dic6—22no—
120C3×#627—22no—
121C3×#627—22no—
122C3×D3×Dic3—22no—
123C3×D3×Dic3Q814yescomplemented
124C3×#533—91no—
125#5622—31no—
126#5578—31no—
127C2×C32×Q8—31no—
128C2×C32×Q8—31no—
129C22×C32×C4—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3C2×D311yescharacteristic
136C2×C3×C4×D3C22×C311yescharacteristic
137C2×C3×Dic6—21no—
138C2×C3×Dic6—21no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×C3×Dic6C2×D311yescharacteristic
144C2×C3×Dic6C2×D311yescharacteristic
145C2×C3×Dic6C22×C311yescharacteristic
146C2×C3×Dic6C22×C311yescharacteristic
147C2×#627C22×C311yescharacteristic
148C2×#627C22×C311yescharacteristic
149C2×D3×Dic3C22×C311yescharacteristic
150C2×D3×Dic3C22×C311yescharacteristic
151C32×C4⋊C4—21no—
152C32×C4⋊C4—21no—
153C32×C4⋊C4—21no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4—41no—
159C32×C4⋊C4C2×D311yescharacteristic
160C32×C4⋊C4C2×D311yescharacteristic
161C32×C4⋊C4C22×C311yescharacteristic
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C42—31no—
165C32×C42—31no—
166C32×C42—31no—
167C4⋊(C3⋊Dic3)C22×C311yescharacteristic
168#3750C22×C311yescharacteristic
169#3750C22×C311yescharacteristic
170#3750C22×C311yescharacteristic
171#3750C22×C311yescharacteristic
172C4×C3⋊Dic3C22×C311yescharacteristic
173C3×#217—31no—
174C3×#217—31no—
175C3×(C2×D3)⋊C4—21no—
176C3×(C2×D3)⋊C4—21no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4C2×D311yescharacteristic
180C3×(C2×D3)⋊C4C2×D311yescharacteristic
181C3×(C2×D3)⋊C4C22×C311yescharacteristic
182C3×(C2×D3)⋊C4C22×C311yescharacteristic
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—61no—
190C3×Dic3⋊C4—21no—
191C3×Dic3⋊C4—21no—
192C3×Dic3⋊C4—21no—
193C3×Dic3⋊C4—21no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
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—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×Dic3⋊C4C2×D311yescharacteristic
215C3×Dic3⋊C4C2×D311yescharacteristic
216C3×Dic3⋊C4C2×D311yescharacteristic
217C3×Dic3⋊C4C2×D311yescharacteristic
218C3×Dic3⋊C4C22×C311yescharacteristic
219C3×Dic3⋊C4C22×C311yescharacteristic
220C3×Dic3⋊C4C22×C311yescharacteristic
221C3×Dic3⋊C4C22×C311yescharacteristic
222C3×C4×Dic3—21no—
223C3×C4×Dic3—21no—
224C3×C4×Dic3—21no—
225C3×C4×Dic3—31no—
226C3×C4×Dic3—31no—
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229C3×C4×Dic3—31no—
230C3×C4×Dic3—31no—
231C3×C4×Dic3—31no—
232C3×C4×Dic3—31no—
233C3×C4×Dic3—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—61no—
236C3×C4×Dic3C2×D311yescharacteristic
237C3×C4×Dic3C2×D311yescharacteristic
238C3×C4×Dic3C2×D311yescharacteristic
239C3×C4×Dic3C22×C311yescharacteristic
240C3×C4×Dic3C22×C311yescharacteristic
241C3×C4×Dic3C22×C311yescharacteristic
242#3724C22×C311yescharacteristic
243#3724C22×C311yescharacteristic
244Dic3⋊Dic3C22×C311yescharacteristic
245Dic3⋊Dic3C22×C311yescharacteristic
246Dic3⋊Dic3C22×C311yescharacteristic
247Dic3⋊Dic3C22×C311yescharacteristic
248(C2×D3)⋊Dic3C22×C311yescharacteristic
249(C2×D3)⋊Dic3C22×C311yescharacteristic
250Dic32C22×C311yescharacteristic
251Dic32C22×C311yescharacteristic
252Dic32C22×C311yescharacteristic
253Dic32C22×C311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C32×D3—21no—
256C2×C32×D3—21no—
257C2×C32×D3C2×Q812yes—
258C33×C4—21no—
259C33×C4—21no—
260C33×C4—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3C2×Q812yes—
265C32×Dic3—21no—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3C2×Q812yes—
270C32×Dic3#4112yes—
271C32×Dic3#4112yes—
272C3×C4⋊Q8—91no—
273C3×C4⋊Q8—91no—
274C3×#125—91no—
275C3×#125—91no—
276C3×C22⋊Q8—31no—
277C3×C22⋊Q8—31no—
278C3×C22⋊Q8—61no—
279C3×C22⋊Q8—91no—
280C3×C22⋊Q8—91no—
281C3×C22⋊Q8—91no—
282C3×C4×Q8—31no—
283C3×C4×Q8—31no—
284C3×C4×Q8—61no—
285C3×C4×Q8—91no—
286C3×C4×Q8—91no—
287C3×C4×Q8—91no—
288C3×#117—91no—
289C3×#117—91no—
290C2×C3×C42—91no—
291#946—31no—
292Q8×Dic3—31no—
293#944—31no—
294#944—31no—
295#924—31no—
296C2×C4×Dic3—31no—
297#897—31no—
298#896—31no—
299#896C3×D311yescharacteristic
300#889—31no—
301#889—31no—
302#889—31no—
303#889—31no—
304#889—61no—
305#888—31no—
306#888—31no—
307#887—31no—
308#887—31no—
309#887C3×D311yescharacteristic, complemented
310#878—31no—
311#878—31no—
312#877—31no—
313#877—31no—
314#872—31no—
315#872—31no—
316C42×D3—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C23×C32—31no—
321C22×C3×D3—21no—
322C22×C3×D3C22×D311yescharacteristic
323C22×C3×D3C23×C311yescharacteristic
324C32×Q8—62no—
325C32×Q8—62no—
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—41no—
343C2×C32×C4—41no—
344C2×C32×C4—41no—
345C2×C32×C4—62no—
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
358C2×C3⋊Dic3C23×C311yescharacteristic
359C2×C3×Dic3—21no—
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—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—34no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—62no—
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C23×C311yescharacteristic
388C2×C3×Dic3C23×C311yescharacteristic
389C2×C3×Dic3C23×C311yescharacteristic
390C2×C3×Dic3C23×C311yescharacteristic
391C2×C3×Dic3C23×C311yescharacteristic
392C2×C3×Dic3C23×C311yescharacteristic
393C2×C3×Dic3C23×C311yescharacteristic
394C3×C4×D3—22no—
395C3×C4×D3—22no—
396C3×C4×D3—34no—
397C3×C4×D3—42no—
398C3×C4×D3—62no—
399C3×Dic6—24no—
400C3×Dic6—22no—
401C3×Dic6—22no—
402C3×Dic6—22no—
403C3×Dic6—22no—
404C3×Dic6—42no—
405C3×Dic6—62no—
406C3×Dic6—62no—
407C3×Dic6—62no—
408C3×Dic6—62no—
409#627—22no—
410#627—22no—
411D3×Dic3—22no—
412D3×Dic3C3×Q814yescomplemented
413#533—91noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C32×D3—22no—
418C2×C3×Q8—31no—
419C2×C3×Q8—31no—
420C2×C3×Q8—31no—
421C2×C3×Q8—31no—
422C2×C3×Q8—61no—
423C2×C3×Q8—61no—
424C2×C3×Q8—91no—
425C2×C3×Q8—91no—
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—61no—
429C22×C3×C4—91no—
430C22×C3×C4—91no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3C2×C3×D311yescharacteristic
436C2×Dic6—31no—
437C2×Dic6—31no—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6C2×C3×D311yescharacteristic
441C2×Dic6C2×C3×D311yescharacteristic
442C3×C4⋊C4—21no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—31no—
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—41no—
454C3×C4⋊C4—61no—
455C3×C4⋊C4—61no—
456C3×C4⋊C4—61no—
457C3×C4⋊C4—61no—
458C3×C4⋊C4—91no—
459C3×C4⋊C4—91no—
460C3×C4⋊C4—91no—
461C3×C4⋊C4—91no—
462C3×C4⋊C4—91no—
463C3×C4⋊C4—91no—
464C3×C4⋊C4—91no—
465C3×C4⋊C4—91no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4D3211yescharacteristic
470C3×C4⋊C4C2×C3×D311yescharacteristic
471C3×C4⋊C4C2×C3×D311yescharacteristic
472C3×C22⋊C4—31no—
473C3×C22⋊C4—31no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—61no—
477C3×C22⋊C4—61no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C42—31no—
481C3×C42—31no—
482C3×C42—31no—
483C3×C42—31no—
484C3×C42—31no—
485C3×C42—31no—
486C3×C42—61no—
487C3×C42—61no—
488C3×C42—61no—
489C3×C42—91no—
490C3×C42—91no—
491C3×C42—91no—
492C3×C42—91no—
493C3×C42—91no—
494#217—31no—
495#217—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4C2×C3×D311yescharacteristic
499(C2×D3)⋊C4C2×C3×D311yescharacteristic
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—31no—
503C4⋊Dic3—31no—
504C4⋊Dic3—31no—
505C4⋊Dic3—31no—
506C4⋊Dic3—61no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—31no—
520Dic3⋊C4—31no—
521Dic3⋊C4—31no—
522Dic3⋊C4—31no—
523Dic3⋊C4—61no—
524Dic3⋊C4—61no—
525Dic3⋊C4—61no—
526Dic3⋊C4—61no—
527Dic3⋊C4C2×C3×D311yescharacteristic
528Dic3⋊C4C2×C3×D311yescharacteristic
529Dic3⋊C4C2×C3×D311yescharacteristic
530Dic3⋊C4C2×C3×D311yescharacteristic
531C4×Dic3—31no—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—31no—
540C4×Dic3—31no—
541C4×Dic3—61no—
542C4×Dic3C2×C3×D311yescharacteristic
543C4×Dic3C2×C3×D311yescharacteristic
544C4×Dic3C2×C3×D311yescharacteristic
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—32no—
549C22×C32—41no—
550C22×C32—61no—
551C22×C32—61no—
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C22×C32C24×C311yescharacteristic
555C2×C3×D3—21no—
556C2×C3×D3—21no—
557C2×C3×D3—21no—
558C2×C3×D3—21no—
559C2×C3×D3—22no—
560C2×C3×D3—41no—
561C2×C3×D3—41no—
562C2×C3×D3D3×Q812yes—
563C2×C3×D3C2×C3×Q812yes—
564C32×C4—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—21no—
570C32×C4—21no—
571C32×C4—21no—
572C32×C4—21no—
573C32×C4—21no—
574C32×C4—32no—
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—81no—
591C32×C4—81no—
592C3⋊Dic3—21no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3C2×C3×Q812yes—
596C3×Dic3—22no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—21no—
605C3×Dic3—22no—
606C3×Dic3—22no—
607C3×Dic3—22no—
608C3×Dic3—32no—
609C3×Dic3—32no—
610C3×Dic3—41no—
611C3×Dic3—41no—
612C3×Dic3—41no—
613C3×Dic3—62no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—121no—
621C3×Dic3—121no—
622C3×Dic3—121no—
623C3×Dic3#23512yes—
624C3×Dic3#23712yes—
625C3×Dic3D3×Q812yes—
626C3×Dic3C2×C3×Q812yes—
627C3×Dic3C3×#4112yes—
628C3×Dic3C3×#4112yes—
629C4⋊Q8—91no—
630C4⋊Q8—91no—
631#125—91no—
632#125—91no—
633C22⋊Q8—31no—
634C22⋊Q8—91no—
635C22⋊Q8—91no—
636C22⋊Q8—91no—
637C4×Q8—31no—
638C4×Q8—91no—
639C4×Q8—91no—
640C4×Q8—91no—
641#117—91no—
642#117—91no—
643C2×C42—91no—
644C33#53311yescharacteristic, complemented, Sylow
645C23×C3—31no—
646C23×C3—31no—
647C23×C3—61no—
648C22×D3C22×C3×D311yescharacteristic
649C3×Q8—62no—
650C3×Q8—62no—
651C3×Q8—62no—
652C3×Q8—62no—
653C3×Q8—64no—
654C3×Q8—122no—
655C3×Q8—182no—
656C3×Q8—182no—
657C2×C3×C4—21no—
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—31no—
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—41no—
681C2×C3×C4—41no—
682C2×C3×C4—41no—
683C2×C3×C4—61no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—94no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—122no—
698C2×C3×C4—182no—
699C2×C3×C4C2×D3211yescharacteristic
700C2×C3×C4C2×D3211yescharacteristic
701C2×C3×C4C2×D3211yescharacteristic
702C2×C3×C4C22×C3×D311yescharacteristic
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×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—34no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—62no—
722C2×Dic3C22×C3×D311yescharacteristic
723C2×Dic3C22×C3×D311yescharacteristic
724C2×Dic3C22×C3×D311yescharacteristic
725C2×Dic3C22×C3×D311yescharacteristic
726C2×Dic3C22×C3×D311yescharacteristic
727C2×Dic3C22×C3×D311yescharacteristic
728C2×Dic3C22×C3×D311yescharacteristic
729C4×D3—22no—
730C4×D3—34no—
731C4×D3—62no—
732Dic6—22no—
733Dic6—22no—
734Dic6—62no—
735Dic6—62no—
736Dic6—62no—
737Dic6—62no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32—62no—
751C2×C32C2×#23511yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32D3×#4111yescharacteristic
756C2×C32D3×#4111yescharacteristic
757C2×C32C22×C3×Q811yescharacteristic
758C2×C32C2×C3×#4111yescharacteristic
759C2×C32C2×C3×#4111yescharacteristic
760C3×D3—22no—
761C3×D3—22no—
762C3×D3—42no—
763C2×Q8—31no—
764C2×Q8—31no—
765C2×Q8—91no—
766C2×Q8—91no—
767C22×C4—31no—
768C22×C4—91no—
769C22×C4—91no—
770C4⋊C4—31no—
771C4⋊C4—31no—
772C4⋊C4—31no—
773C4⋊C4—31no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—91no—
779C4⋊C4—91no—
780C4⋊C4—91no—
781C4⋊C4—91no—
782C4⋊C4—91no—
783C4⋊C4—91no—
784C4⋊C4—91no—
785C4⋊C4C3×D3211yescharacteristic
786C22⋊C4—31no—
787C22⋊C4—31no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C42—31no—
791C42—31no—
792C42—31no—
793C42—91no—
794C42—91no—
795C42—91no—
796C42—91no—
797C42—91no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—32no—
802C22×C3—32no—
803C22×C3—41no—
804C22×C3—62no—
805C22×C3—61no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—61no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3C22×D3211yescharacteristic
812C22×C3C23×C3×D311yescharacteristic
813C22×C3C23×C3×D311yescharacteristic
814C2×D3—21no—
815C2×D3—21no—
816C2×D3C3×D3×Q812yes—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—32no—
828C3×C4—32no—
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—62no—
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—81no—
855C3×C4—81no—
856C3×C4—92no—
857C3×C4—121no—
858C3×C4—121no—
859C3×C4—121no—
860C3×C4—181no—
861C3×C4—181no—
862C3×C4—181no—
863Dic3—21no—
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—32no—
868Dic3—32no—
869Dic3—62no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—121no—
877Dic3—121no—
878Dic3—121no—
879Dic3C3×#23512yes—
880Dic3C3×#23712yes—
881Dic3C3×D3×Q812yes—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32#557811yescharacteristic, complemented
887C32#562211yescharacteristic, complemented
888C32C3×#53311yescharacteristic, complemented
889C23—31no—
890Q8—62no—
891Q8—62no—
892Q8—182no—
893Q8—182no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—31no—
901C2×C4—62no—
902C2×C4—94no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—182no—
908C2×C4C2×C3×D3211yescharacteristic
909C2×C4C2×C3×D3211yescharacteristic
910C2×C4C2×C3×D3211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—41no—
923C2×C3—62no—
924C2×C3—62no—
925C2×C3—122no—
926C2×C3D3×#23511yescharacteristic
927C2×C3D3×#23711yescharacteristic
928C2×C3D32×Q811yescharacteristic
929C2×C3C2×C3×#23511yescharacteristic
930C2×C3C2×C3×#23711yescharacteristic
931C2×C3C2×C3×D3×Q811yescharacteristic
932C2×C3C2×C3×D3×Q811yescharacteristic
933C2×C3C3×D3×#4111yescharacteristic
934C2×C3C3×D3×#4111yescharacteristic
935D3—22no—
936C22—32no—
937C22—61no—
938C22—61no—
939C22C22×C3×D3211yescharacteristic
940C4—21no—
941C4—21no—
942C4—21no—
943C4—32no—
944C4—32no—
945C4—32no—
946C4—61no—
947C4—61no—
948C4—61no—
949C4—61no—
950C4—92no—
951C4—181no—
952C4—181no—
953C4—181no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3#1059438611yescharacteristic, direct product factor
959C3C3×#557811yescharacteristic, complemented
960C3C3×#562211yescharacteristic, complemented
961C2—62no—
962C2C3×D3×#23511yescharacteristic
963C2C3×D3×#23711yescharacteristic
964C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64098C2semidirect
3. C32×#887C2semidirect
9. C3×#63870C2semidirect
11. C3×Dic3×Dic6C2semidirect
12. C3×#63839C2semidirect
13. C3×#63839C2semidirect
14. C3×#63837C2semidirect
15. C3×#63837C2semidirect
18. #10594386C3direct (N × H)
56. #64098C2×C3semidirect
78. C3×#887D3semidirect
79. C3×#887C2×C3semidirect
95. #63870C2×C3semidirect
97. Dic3×Dic6C2×C3semidirect
98. #63839C2×C3semidirect
99. #63839C2×C3semidirect
100. #63837C2×C3semidirect
101. #63837C2×C3semidirect
123. C3×D3×Dic3Q8semidirect
309. #887C3×D3semidirect
412. D3×Dic3C3×Q8semidirect
644. C33#533semidirect
886. C32#5578semidirect
887. C32#5622semidirect
888. C32C3×#533semidirect
958. C3#10594386direct (N × H)
959. C3C3×#5578semidirect
960. C3C3×#5622semidirect

Maximal subgroups

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

subgroupindex
C3×#640982
C32×#8962
C32×#8872
C3×#638932
C3×#638872
C3×#638772
C3×C4×D3×Dic32
C3×#638702
C3×#638512
C3×Dic3×Dic62
C3×#638392
C3×#638372
C3×#56223
C3×#55783
#105943863