Finite Group Databasebeta

← C3×#69414 #11773390

Subgroups — C3×#69414 #11773390

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×C3×C3⋊#95C211yesmaximal, characteristic
8C3×#1442—31nomaximal
9#69414C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—22no—
18C2×C3×Dic3⋊C4—22no—
19C2×C3×Dic3⋊C4—22no—
20C32×#95—22no—
21C3×C3⋊#95—22no—
22C3×C3⋊#95—22no—
23C3×C3⋊#95—22no—
24C3×C3⋊#95—22no—
25C3×C3⋊#95C414yescomplemented
26C22×C3×C4⋊C4—31no—
27C22×Dic3⋊C4C2×C311yescharacteristic
28C2×C3×#95—21no—
29C2×C3×#95—31no—
30C2×C3×#95—31no—
31C2×C3×#95—31no—
32C2×C3×#95—31no—
33C2×C3×#95—31no—
34C2×C3×#95D311yescharacteristic
35C2×C3×#95C2×C311yescharacteristic
36C2×C3⋊#95C2×C311yescharacteristic
37C2×C3⋊#95C2×C311yescharacteristic
38C2×C3⋊#95C2×C311yescharacteristic
39C2×C3⋊#95C2×C311yescharacteristic
40C2×C3⋊#95C2×C311yescharacteristic
41C24×C32C2311yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4C2×C412yes—
61C22×C32×C4D412yes—
62C22×C32×C4Q812yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3C2×C412yes—
86C22×C3×Dic3C2×C412yes—
87C22×C3×Dic3D412yes—
88C22×C3×Dic3D412yes—
89C22×C3×Dic3D412yes—
90C22×C3×Dic3Q812yes—
91C3×Dic3⋊C4—28no—
92#1442—31noSylow
93C23×C3×C4—21no—
94C23×C3×C4—21no—
95C23×C3×C4—21no—
96C23×C3×C4—31no—
97C23×C3×C4—31no—
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C22×C311yescharacteristic
104C23×C3×C4C22×C311yescharacteristic
105C23×C3×C4C22×C311yescharacteristic
106C23×Dic3C22×C311yescharacteristic
107C23×Dic3C22×C311yescharacteristic
108C23×Dic3C22×C311yescharacteristic
109C23×Dic3C22×C311yescharacteristic
110C2×C3×C4⋊C4—62no—
111C2×C3×C4⋊C4—62no—
112C2×C3×C4⋊C4—62no—
113C2×Dic3⋊C4—22no—
114C2×Dic3⋊C4—22no—
115C2×Dic3⋊C4—22no—
116C3×#95—24no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—34no—
120C3×#95—62no—
121C3×#95—62no—
122C3×#95—62no—
123C3×#95—62no—
124C3⋊#95—22no—
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95C3×C414yescomplemented
129C23×C32C22×C411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×D411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32C2×Q811yescharacteristic
135C23×C32C2×Q811yescharacteristic
136C23×C32#4111yescharacteristic
137C23×C32#4111yescharacteristic
138C23×C32#4111yescharacteristic
139C23×C32#4111yescharacteristic
140C23×C32#4111yescharacteristic
141C23×C32#4111yescharacteristic
142C23×C32#4111yescharacteristic
143C23×C32#4111yescharacteristic
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4—41no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4—41no—
160C2×C32×C4—41no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C2×C3×Dic3—41no—
183C2×C3×Dic3—41no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C2×C3×Dic3—41no—
187C2×C3×Dic3—41no—
188C2×C3×Dic3—41no—
189C2×C3×Dic3—41no—
190C2×C3×Dic3—41no—
191C2×C3×Dic3—41no—
192C2×C3×Dic3C4⋊C414yes—
193C22×C4⋊C4—31no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95C3×D311yescharacteristic
200C24×C3—21no—
201C24×C3C22×D311yescharacteristic
202C24×C3C23×C311yescharacteristic
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—32no—
249C22×C3×C4—32no—
250C22×C3×C4—32no—
251C22×C3×C4—32no—
252C22×C3×C4—32no—
253C22×C3×C4—32no—
254C22×C3×C4—41no—
255C22×C3×C4—41no—
256C22×C3×C4—41no—
257C22×C3×C4—41no—
258C22×C3×C4—41no—
259C22×C3×C4—41no—
260C22×C3×C4—41no—
261C22×C3×C4—41no—
262C22×C3×C4—41no—
263C22×C3×C4—41no—
264C22×C3×C4—41no—
265C22×C3×C4—41no—
266C22×C3×C4—61no—
267C22×C3×C4—61no—
268C22×C3×C4—61no—
269C22×C3×C4—61no—
270C22×C3×C4—61no—
271C22×C3×C4—61no—
272C22×C3×C4—61no—
273C22×C3×C4—61no—
274C22×C3×C4—61no—
275C22×C3×C4—61no—
276C22×C3×C4—61no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4—61no—
280C22×C3×C4—61no—
281C22×C3×C4—61no—
282C22×C3×C4—61no—
283C22×C3×C4—61no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C22×C3×C4Dic612yes—
289C22×C3×C4C4×D312yes—
290C22×C3×C4#6712yes—
291C22×C3×C4C2×C3×C412yes—
292C22×C3×C4C3×D412yes—
293C22×C3×C4C3×Q812yes—
294C22×Dic3—21no—
295C22×Dic3—21no—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3C2×C3×C412yes—
317C22×Dic3C2×C3×C412yes—
318C22×Dic3C3×D412yes—
319C22×Dic3C3×D412yes—
320C22×Dic3C3×D412yes—
321C22×Dic3C3×Q812yes—
322C3×C4⋊C4—68no—
323Dic3⋊C4—28no—
324C22×C32C2×C4⋊C411yescharacteristic
325C22×C32#11711yescharacteristic
326C22×C32#11711yescharacteristic
327C22×C32C4×D411yescharacteristic
328C22×C32C4×D411yescharacteristic
329C22×C32C4×D411yescharacteristic
330C22×C32C4×Q811yescharacteristic
331C22×C32#12011yescharacteristic
332C22×C32#12111yescharacteristic
333C22×C32#12111yescharacteristic
334C22×C32#12111yescharacteristic
335C22×C32C22⋊Q811yescharacteristic
336C22×C32C22⋊Q811yescharacteristic
337C22×C32C22⋊Q811yescharacteristic
338C22×C32C22⋊Q811yescharacteristic
339C22×C32C22⋊Q811yescharacteristic
340C22×C32#12311yescharacteristic
341C22×C32#12311yescharacteristic
342C22×C32#12311yescharacteristic
343C22×C32#12311yescharacteristic
344C22×C32#12311yescharacteristic
345C22×C32#12411yescharacteristic
346C22×C32#12411yescharacteristic
347C22×C32#12411yescharacteristic
348C22×C32#12411yescharacteristic
349C22×C32#12511yescharacteristic
350C22×C32#12511yescharacteristic
351C22×C32#12511yescharacteristic
352C22×C32#12511yescharacteristic
353C22×C32#12511yescharacteristic
354C22×C32#12611yescharacteristic
355C22×C32#12611yescharacteristic
356C22×C32#12611yescharacteristic
357C22×C32#12611yescharacteristic
358C22×C32C4⋊Q811yescharacteristic
359C32×C4—42no—
360C32×C4—42no—
361C32×C4—42no—
362C3×Dic3—24no—
363C3×Dic3—42no—
364C3×Dic3—42no—
365C3×Dic3—42no—
366C23×C4—31no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4C2×C3×D311yescharacteristic
371C23×C4C2×C3×D311yescharacteristic
372C23×C4C2×C3×D311yescharacteristic
373C2×C4⋊C4—62no—
374C2×C4⋊C4—62no—
375C2×C4⋊C4—62no—
376#95—22no—
377#95—34no—
378#95—62no—
379#95—62no—
380#95—62no—
381#95—62no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3C2×Dic611yescharacteristic
398C23×C3C2×C4×D311yescharacteristic
399C23×C3#23511yescharacteristic
400C23×C3#23511yescharacteristic
401C23×C3#23511yescharacteristic
402C23×C3#23511yescharacteristic
403C23×C3D3×D411yescharacteristic
404C23×C3D3×D411yescharacteristic
405C23×C3D3×D411yescharacteristic
406C23×C3#23711yescharacteristic
407C23×C3#23711yescharacteristic
408C23×C3#23711yescharacteristic
409C23×C3D3×Q811yescharacteristic
410C23×C3#23911yescharacteristic
411C23×C3C2×#6711yescharacteristic
412C23×C3C22×C3×C411yescharacteristic
413C23×C3C2×C3×D411yescharacteristic
414C23×C3C2×C3×D411yescharacteristic
415C23×C3C2×C3×D411yescharacteristic
416C23×C3C2×C3×D411yescharacteristic
417C23×C3C2×C3×Q811yescharacteristic
418C23×C3C2×C3×Q811yescharacteristic
419C23×C3C3×#4111yescharacteristic
420C23×C3C3×#4111yescharacteristic
421C23×C3C3×#4111yescharacteristic
422C23×C3C3×#4111yescharacteristic
423C23×C3C3×#4111yescharacteristic
424C23×C3C3×#4111yescharacteristic
425C23×C3C3×#4111yescharacteristic
426C23×C3C3×#4111yescharacteristic
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—34no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—42no—
453C2×C3×C4—42no—
454C2×C3×C4—42no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—62no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—121no—
507C2×C3×C4—121no—
508C2×C3×C4—121no—
509C2×C3×C4—121no—
510C2×C3×C4—121no—
511C2×C3×C4—121no—
512C2×C3×C4—121no—
513C2×C3×C4—121no—
514C2×C3×C4—121no—
515C2×C3×C4—121no—
516C2×C3×C4—121no—
517C2×C3×C4—121no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3C3×C4⋊C414yes—
546C2×C32#38211yescharacteristic
547C2×C32#38511yescharacteristic
548C2×C32#38711yescharacteristic
549C2×C32#38711yescharacteristic
550C2×C32#38811yescharacteristic
551C2×C32#38811yescharacteristic
552C2×C32#38911yescharacteristic
553C2×C32#39311yescharacteristic
554C2×C32#39411yescharacteristic
555C2×C32#39711yescharacteristic
556C2×C32#39811yescharacteristic
557C2×C32#39811yescharacteristic
558C2×C32#40011yescharacteristic
559C2×C32#40011yescharacteristic
560C2×C32#40011yescharacteristic
561C24C22×C3×D311yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—32no—
583C22×C4—32no—
584C22×C4—32no—
585C22×C4—32no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4C3×Dic612yes—
609C22×C4C3×C4×D312yes—
610C22×C4C3×#6712yes—
611C4⋊C4—68no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3C4×Dic611yescharacteristic
648C22×C3#87011yescharacteristic
649C22×C3#87211yescharacteristic
650C22×C3#87611yescharacteristic
651C22×C3#87711yescharacteristic
652C22×C3#87811yescharacteristic
653C22×C3#87811yescharacteristic
654C22×C3#87911yescharacteristic
655C22×C3#67⋊C411yescharacteristic
656C22×C3#88311yescharacteristic
657C22×C3#88311yescharacteristic
658C22×C3#88411yescharacteristic
659C22×C3#88411yescharacteristic
660C22×C3#88511yescharacteristic
661C22×C3#88511yescharacteristic
662C22×C3#88511yescharacteristic
663C22×C3#88811yescharacteristic
664C22×C3#88911yescharacteristic
665C22×C3#88911yescharacteristic
666C22×C3#88911yescharacteristic
667C22×C3#89011yescharacteristic
668C22×C3D3×C4⋊C411yescharacteristic
669C22×C3#89311yescharacteristic
670C22×C3#89411yescharacteristic
671C22×C3#89411yescharacteristic
672C22×C3#89611yescharacteristic
673C22×C3#89811yescharacteristic
674C22×C3#89811yescharacteristic
675C22×C3#92411yescharacteristic
676C22×C3C4×#6711yescharacteristic
677C22×C3#92911yescharacteristic
678C22×C3#93611yescharacteristic
679C22×C3#93711yescharacteristic
680C22×C3#93911yescharacteristic
681C22×C3#94611yescharacteristic
682C22×C3C2×C3×C4⋊C411yescharacteristic
683C22×C3C3×#11711yescharacteristic
684C22×C3C3×#11711yescharacteristic
685C22×C3C3×C4×D411yescharacteristic
686C22×C3C3×C4×D411yescharacteristic
687C22×C3C3×C4×D411yescharacteristic
688C22×C3C3×C4×Q811yescharacteristic
689C22×C3C3×#12011yescharacteristic
690C22×C3C3×#12111yescharacteristic
691C22×C3C3×#12111yescharacteristic
692C22×C3C3×#12111yescharacteristic
693C22×C3C3×C22⋊Q811yescharacteristic
694C22×C3C3×C22⋊Q811yescharacteristic
695C22×C3C3×C22⋊Q811yescharacteristic
696C22×C3C3×C22⋊Q811yescharacteristic
697C22×C3C3×C22⋊Q811yescharacteristic
698C22×C3C3×#12311yescharacteristic
699C22×C3C3×#12311yescharacteristic
700C22×C3C3×#12311yescharacteristic
701C22×C3C3×#12311yescharacteristic
702C22×C3C3×#12311yescharacteristic
703C22×C3C3×#12411yescharacteristic
704C22×C3C3×#12411yescharacteristic
705C22×C3C3×#12411yescharacteristic
706C22×C3C3×#12411yescharacteristic
707C22×C3C3×#12511yescharacteristic
708C22×C3C3×#12511yescharacteristic
709C22×C3C3×#12511yescharacteristic
710C22×C3C3×#12511yescharacteristic
711C22×C3C3×#12511yescharacteristic
712C22×C3C3×#12611yescharacteristic
713C22×C3C3×#12611yescharacteristic
714C22×C3C3×#12611yescharacteristic
715C22×C3C3×#12611yescharacteristic
716C22×C3C3×C4⋊Q811yescharacteristic
717C3×C4—44no—
718C3×C4—44no—
719C3×C4—44no—
720C3×C4—42no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—64no—
727C3×C4—122no—
728C3×C4—122no—
729C3×C4—122no—
730Dic3—24no—
731Dic3—42no—
732Dic3—42no—
733Dic3—42no—
734C32#144211yescharacteristic, complemented, Sylow
735C23C2×C3×Dic611yescharacteristic
736C23C2×C3×C4×D311yescharacteristic
737C23C3×#23511yescharacteristic
738C23C3×#23511yescharacteristic
739C23C3×#23511yescharacteristic
740C23C3×#23511yescharacteristic
741C23C3×D3×D411yescharacteristic
742C23C3×D3×D411yescharacteristic
743C23C3×D3×D411yescharacteristic
744C23C3×#23711yescharacteristic
745C23C3×#23711yescharacteristic
746C23C3×#23711yescharacteristic
747C23C3×D3×Q811yescharacteristic
748C23C3×#23911yescharacteristic
749C23C2×C3×#6711yescharacteristic
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—34no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4—121no—
793C2×C4—121no—
794C2×C4—121no—
795C2×C4—121no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3#464711yescharacteristic
815C2×C3#465011yescharacteristic
816C2×C3#465411yescharacteristic
817C2×C3#465711yescharacteristic
818C2×C3#465811yescharacteristic
819C2×C3#466011yescharacteristic
820C2×C3#466911yescharacteristic
821C2×C3#467511yescharacteristic
822C2×C3#493311yescharacteristic
823C2×C3#494511yescharacteristic
824C2×C3#494711yescharacteristic
825C2×C3#495911yescharacteristic
826C2×C3#498211yescharacteristic
827C2×C3#498511yescharacteristic
828C2×C3#498911yescharacteristic
829C2×C3C3×#38211yescharacteristic
830C2×C3C3×#38511yescharacteristic
831C2×C3C3×#38711yescharacteristic
832C2×C3C3×#38711yescharacteristic
833C2×C3C3×#38811yescharacteristic
834C2×C3C3×#38811yescharacteristic
835C2×C3C3×#38911yescharacteristic
836C2×C3C3×#39311yescharacteristic
837C2×C3C3×#39411yescharacteristic
838C2×C3C3×#39711yescharacteristic
839C2×C3C3×#39811yescharacteristic
840C2×C3C3×#39811yescharacteristic
841C2×C3C3×#40011yescharacteristic
842C2×C3C3×#40011yescharacteristic
843C2×C3C3×#40011yescharacteristic
844C22C3×C4×Dic611yescharacteristic
845C22C3×#87011yescharacteristic
846C22C3×#87211yescharacteristic
847C22C3×#87611yescharacteristic
848C22C3×#87711yescharacteristic
849C22C3×#87811yescharacteristic
850C22C3×#87811yescharacteristic
851C22C3×#87911yescharacteristic
852C22C3×#67⋊C411yescharacteristic
853C22C3×#88311yescharacteristic
854C22C3×#88311yescharacteristic
855C22C3×#88411yescharacteristic
856C22C3×#88411yescharacteristic
857C22C3×#88511yescharacteristic
858C22C3×#88511yescharacteristic
859C22C3×#88511yescharacteristic
860C22C3×#88811yescharacteristic
861C22C3×#88911yescharacteristic
862C22C3×#88911yescharacteristic
863C22C3×#88911yescharacteristic
864C22C3×#89011yescharacteristic
865C22C3×D3×C4⋊C411yescharacteristic
866C22C3×#89311yescharacteristic
867C22C3×#89411yescharacteristic
868C22C3×#89411yescharacteristic
869C22C3×#89611yescharacteristic
870C22C3×#89811yescharacteristic
871C22C3×#89811yescharacteristic
872C22C3×#92411yescharacteristic
873C22C3×C4×#6711yescharacteristic
874C22C3×#92911yescharacteristic
875C22C3×#93611yescharacteristic
876C22C3×#93711yescharacteristic
877C22C3×#93911yescharacteristic
878C22C3×#94611yescharacteristic
879C4—42no—
880C4—42no—
881C4—42no—
882C4—64no—
883C4—122no—
884C4—122no—
885C4—122no—
886C3—21no—
887C3#6941411yescharacteristic, direct product factor
888C3C3×#144211yescharacteristic, complemented
889C2C3×#464711yescharacteristic
890C2C3×#465011yescharacteristic
891C2C3×#465411yescharacteristic
892C2C3×#465711yescharacteristic
893C2C3×#465811yescharacteristic
894C2C3×#466011yescharacteristic
895C2C3×#466911yescharacteristic
896C2C3×#467511yescharacteristic
897C2C3×#493311yescharacteristic
898C2C3×#494511yescharacteristic
899C2C3×#494711yescharacteristic
900C2C3×#495911yescharacteristic
901C2C3×#498211yescharacteristic
902C2C3×#498511yescharacteristic
903C2C3×#498911yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1442
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
9. #69414C3direct (N × H)
25. C3×C3⋊#95C4semidirect
128. C3⋊#95C3×C4semidirect
734. C32#1442semidirect
887. C3#69414direct (N × H)
888. C3C3×#1442semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14423
#694143