Finite Group Databasebeta

← C3×#79816 #11896290

Subgroups — C3×#79816 #11896290

Order 1152.

742 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5585C211yesmaximal, characteristic
2C3×#5569C211yesmaximal, characteristic, complemented
3C32×#441C211yesmaximal, characteristic, complemented
4C3×#5185C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6C3×#5027C211yesmaximal, characteristic
7C3×#5022C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4870C211yesmaximal, characteristic, complemented
10C3×#4817C211yesmaximal, characteristic, complemented
11C3×#4800C211yesmaximal, characteristic, complemented
12C3×#4794C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×#4713C211yesmaximal, characteristic
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3371—31nomaximal
17#79816C311yesmaximal, characteristic, direct product factor
18C2×C32×Q16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×#947C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#894—21no—
28C3×#894—21no—
29C3×#893C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#890—21no—
32C3×#890C2211yescharacteristic
33C3×#888—21no—
34C3×#888C2211yescharacteristic
35C3×#875—21no—
36C3×#874C2211yescharacteristic
37C3×C4×D12—21no—
38C3×#870—21no—
39C3×#870C2211yescharacteristic
40C3×C4×Dic6—21no—
41C3×C4×Dic6C2211yescharacteristic
42C32×#106C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#97C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#557—31no—
63#5585C2×C311yescharacteristic
64#5569C2×C311yescharacteristic, complemented
65C3×#490—31no—
66C3×#489—31no—
67C3×#488—31no—
68C3×#479—31no—
69C3×#478—31no—
70C3×#476—31no—
71C3×#464—31no—
72C3×#464—31no—
73C3×#460—31no—
74C3×#446—31no—
75C3×#441—21no—
76C3×#441D311yescharacteristic, complemented
77C3×#441C2×C311yescharacteristic, complemented
78C3×#440—31no—
79C3×C4×SD16—31no—
80#5185C2×C311yescharacteristic, complemented
81#5185C2×C311yescharacteristic, complemented
82#5027C2×C311yescharacteristic
83#5022C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4870C2×C311yescharacteristic, complemented
86#4817C2×C311yescharacteristic, complemented
87#4800C2×C311yescharacteristic, complemented
88#4794C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90#4713C2×C311yescharacteristic
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6D411yescharacteristic
102C32×Q16—22no—
103C2×C32×C8C2311yescharacteristic
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C42—21no—
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112C3×#215—22no—
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3371—31noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16C2×D311yescharacteristic
141C2×C3×Q16C22×C311yescharacteristic
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—61no—
146C3×#127—31no—
147C3×#125—31no—
148C3×#125—31no—
149C3×#125—61no—
150C3×#125—61no—
151C3×#124—31no—
152C3×#124—31no—
153C3×#124—61no—
154C3×#123—61no—
155C3×#123—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8—21no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—61no—
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C2×D311yescharacteristic
164C3×C4×Q8C22×C311yescharacteristic
165C3×C4×Q8C22×C311yescharacteristic
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169#947C22×C311yescharacteristic
170#947C22×C311yescharacteristic
171Q8×Dic3C22×C311yescharacteristic
172Q8×Dic3C22×C311yescharacteristic
173C2×#215C22×C311yescharacteristic
174C2×#215C22×C311yescharacteristic
175#894—21no—
176#894—21no—
177#893C22×C311yescharacteristic
178#893C22×C311yescharacteristic
179#890—21no—
180#890C22×C311yescharacteristic
181#888—21no—
182#888C22×C311yescharacteristic
183#875—21no—
184#874C22×C311yescharacteristic
185C4×D12—21no—
186#870—21no—
187#870C22×C311yescharacteristic
188C4×Dic6—21no—
189C4×Dic6C22×C311yescharacteristic
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic
194C3×#106C22×C311yescharacteristic
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—21no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×#103C22×C311yescharacteristic
205C3×#103C22×C311yescharacteristic
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#97—21no—
213C3×#97—31no—
214C3×#97C2×D311yescharacteristic
215C3×#97C22×C311yescharacteristic
216C3×C4×C8—31no—
217#835C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#821C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#821C22×C311yescharacteristic
223#815C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×Q8#4112yes—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—42no—
256C3×D12—81no—
257C3×C4×D3—81no—
258C3×C4×D3—81no—
259C3×Dic6—41no—
260C3×Dic6—42no—
261C32×C8—21no—
262C32×C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—31no—
267#490—31no—
268#489—31no—
269#488—31no—
270#479—31no—
271#478—31no—
272#476—31no—
273#464—31no—
274#464—31no—
275#460—31no—
276#446—31no—
277#441C3×D311yescharacteristic, complemented
278#440—31no—
279C4×SD16—31no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C23×C311yescharacteristic
287C2×C3×Q8C23×C311yescharacteristic
288C2×C3×D4—31no—
289C2×C3×D4—31no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12C23×C311yescharacteristic
297C2×D12C23×C311yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×Dic6—21no—
301C2×Dic6C3×D411yescharacteristic
302C3×Q16—24no—
303C3×Q16—22no—
304C3×Q16—22no—
305C3×SD16—62no—
306C3×SD16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C23×C311yescharacteristic
314C2×C3×C8C23×C311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—41no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C23×C311yescharacteristic
338C3×C4⋊C4C23×C311yescharacteristic
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42—41no—
354C3×C42—61no—
355C3×C42—61no—
356C3×C42C22×D311yescharacteristic
357C3×C42C23×C311yescharacteristic
358#215—22no—
359#215—22no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3C3×D411yescharacteristic
370C4⋊Dic3C23×C311yescharacteristic
371C4⋊Dic3C23×C311yescharacteristic
372Dic3⋊C4—21no—
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4C3×D411yescharacteristic
377Dic3⋊C4C3×D411yescharacteristic
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3C23×C311yescharacteristic
381C4×Dic3C23×C311yescharacteristic
382C2×C3⋊C8C23×C311yescharacteristic
383C2×C3⋊C8C23×C311yescharacteristic
384C22×C32C22×D411yescharacteristic
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—22no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4C2×#4111yescharacteristic
398C32×C42−1+411yescharacteristic
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C2×Q16C2×C3×D311yescharacteristic
406C2×SD16—31no—
407C2×SD16—31no—
408C4⋊Q8—31no—
409C4⋊Q8—61no—
410#127—31no—
411#125—31no—
412#125—31no—
413#125—61no—
414#125—61no—
415#124—31no—
416#124—31no—
417#124—61no—
418#123—61no—
419#123—61no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—61no—
424C4×Q8C2×C3×D311yescharacteristic
425C4×Q8C2×C3×D311yescharacteristic
426C4×D4—31no—
427C4×D4—31no—
428C4×D4—61no—
429#107—31no—
430#106—31no—
431#106C2×C3×D311yescharacteristic
432C4⋊C8—31no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435#103—31no—
436#103—31no—
437#103C2×C3×D311yescharacteristic
438#103C2×C3×D311yescharacteristic
439#102—31no—
440#102—31no—
441#102—31no—
442#102—31no—
443#102—31no—
444#102—31no—
445#97—31no—
446#97C2×C3×D311yescharacteristic
447C4×C8—31no—
448C23×C3—61no—
449C23×C3—61no—
450C22×D3—21no—
451C22×D3—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—22no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—22no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—121no—
463C3×Q8—122no—
464C3×Q8#23512yes—
465C3×Q8C3×#4112yes—
466C3×D4—61no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—61no—
470C3×D4—122no—
471C3×D4—241no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—241no—
494C2×C3×C4—241no—
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4D3×D411yescharacteristic
497C2×C3×C4C2×C3×D411yescharacteristic
498C2×C3×C4C2×C3×D411yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C24×C311yescharacteristic
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505C2×Dic3C2×C3×D411yescharacteristic
506C2×Dic3C2×C3×D411yescharacteristic
507D12—21no—
508D12—21no—
509D12—21no—
510D12—21no—
511D12—42no—
512D12—81no—
513C4×D3—81no—
514C4×D3—81no—
515Dic6—41no—
516Dic6—42no—
517C3×C8—22no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C2×C32#54811yescharacteristic
528C2×C32#57511yescharacteristic
529C2×C32#57711yescharacteristic
530C3×D3—81no—
531C3×D3—81no—
532C2×Q8—31no—
533C2×Q8—61no—
534C2×Q8C22×C3×D311yescharacteristic
535C2×Q8C22×C3×D311yescharacteristic
536C2×D4—31no—
537C2×D4—31no—
538C2×D4—61no—
539C2×D4—61no—
540C22×C4—61no—
541C22×C4—61no—
542Q16—22no—
543SD16—62no—
544SD16—62no—
545C2×C8—31no—
546C2×C8—31no—
547C2×C8C22×C3×D311yescharacteristic
548C2×C8C22×C3×D311yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4C22×C3×D311yescharacteristic
564C4⋊C4C22×C3×D311yescharacteristic
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C42—21no—
572C42—21no—
573C42—31no—
574C42—31no—
575C42—61no—
576C42—61no—
577C42C22×C3×D311yescharacteristic
578C22×C3—21no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C22×C3×D411yescharacteristic
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—42no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—81no—
616C3×C4—81no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4C2×#23511yescharacteristic
620C3×C4#101011yescharacteristic
621C3×C4C2×C3×#4111yescharacteristic
622C3×C4C3×2−1+411yescharacteristic
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—21no—
627Dic3—41no—
628Dic3—41no—
629C32#337111yescharacteristic, complemented, Sylow
630C23—61no—
631C23—61no—
632Q8—21no—
633Q8—21no—
634Q8—21no—
635Q8—121no—
636Q8—122no—
637Q8C3×#23512yes—
638D4—61no—
639D4—61no—
640D4—61no—
641D4—61no—
642D4—122no—
643D4—241no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—241no—
655C2×C4—241no—
656C2×C4C3×D3×D411yescharacteristic
657C2×C4C3×D3×D411yescharacteristic
658C2×C4C23×C3×D311yescharacteristic
659C8—21no—
660C8—21no—
661C8—61no—
662C8—61no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—241no—
667C2×C3—241no—
668C2×C3#555211yescharacteristic
669C2×C3#577711yescharacteristic
670C2×C3#577811yescharacteristic
671C2×C3C3×#54811yescharacteristic
672C2×C3C3×#57511yescharacteristic
673C2×C3C3×#57711yescharacteristic
674D3—81no—
675D3—81no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22—121no—
681C22—121no—
682C22C2×C3×D3×D411yescharacteristic
683C4—21no—
684C4—21no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—61no—
690C4—61no—
691C4—61no—
692C4—61no—
693C4—121no—
694C4—121no—
695C4C2×C3×#23511yescharacteristic
696C4C3×#101011yescharacteristic
697C3—21no—
698C3#7981611yescharacteristic, direct product factor
699C3C3×#337111yescharacteristic, complemented
700C2—241no—
701C2—241no—
702C2C3×#555211yescharacteristic
703C2C3×#577711yescharacteristic
704C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#441C2
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC3×#441D3
hypocenterC3C3×#3371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#441

Complements

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

NH ≅ G/Ntype
2. C3×#5569C2semidirect
3. C32×#441C2semidirect
4. C3×#5185C2semidirect
5. C3×#5185C2semidirect
7. C3×#5022C2semidirect
8. C3×#4871C2semidirect
9. C3×#4870C2semidirect
10. C3×#4817C2semidirect
11. C3×#4800C2semidirect
12. C3×#4794C2semidirect
13. C3×#4788C2semidirect
15. C3×#4701C2semidirect
17. #79816C3direct (N × H)
64. #5569C2×C3semidirect
76. C3×#441D3semidirect
77. C3×#441C2×C3semidirect
80. #5185C2×C3semidirect
81. #5185C2×C3semidirect
83. #5022C2×C3semidirect
84. #4871C2×C3semidirect
85. #4870C2×C3semidirect
86. #4817C2×C3semidirect
87. #4800C2×C3semidirect
88. #4794C2×C3semidirect
89. #4788C2×C3semidirect
91. #4701C2×C3semidirect
277. #441C3×D3semidirect
629. C32#3371semidirect
698. C3#79816direct (N × H)
699. C3C3×#3371semidirect

Maximal subgroups

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

subgroupindex
C3×#55852
C3×#55692
C32×#4412
C3×#51852
C3×#50272
C3×#50222
C3×#48712
C3×#48702
C3×#48172
C3×#48002
C3×#47942
C3×#47882
C3×#47132
C3×#47012
C3×#33713
#798163