Finite Group Databasebeta

← C3×#79609 #11887368

Subgroups — C3×#79609 #11887368

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5558C211yesmaximal, characteristic, complemented
2C3×#5554C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5156C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4885C211yesmaximal, characteristic, complemented
9C3×#4884C211yesmaximal, characteristic, complemented
10C3×#4778C211yesmaximal, characteristic, complemented
11C3×#4775C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4697C211yesmaximal, characteristic, complemented
15C3×C8×D12C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#79609C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C3×#938C2211yescharacteristic, complemented
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C3×#929—21no—
29C3×C4×#67—21no—
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×D3×C8C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic, complemented
33C3×#897C2211yescharacteristic
34C3×#895C2211yescharacteristic
35C3×#892C2211yescharacteristic, complemented
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#886—21no—
38C3×#884—21no—
39C3×#882—21no—
40C3×#879—21no—
41C3×#875C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×#870C2211yescharacteristic, complemented
44C32×#107C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic, complemented
47C32×C4×C8C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5558C2×C311yescharacteristic, complemented
64#5554C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#484—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#466—31no—
70C3×#465—31no—
71C3×#463—31no—
72C3×#449—31no—
73C3×#447—31no—
74C3×C4×D8—21no—
75C3×C4×D8D311yescharacteristic, complemented
76C3×C4×D8C2×C311yescharacteristic, complemented
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5158C2×C311yescharacteristic, complemented
81#5156C2×C311yescharacteristic, complemented
82#5016C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4885C2×C311yescharacteristic, complemented
85#4884C2×C311yescharacteristic, complemented
86#4778C2×C311yescharacteristic, complemented
87#4775C2×C311yescharacteristic, complemented
88#4772C2×C311yescharacteristic, complemented
89D3×#102C2×C311yescharacteristic, complemented
90#4697C2×C311yescharacteristic, complemented
91C8×D12C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—41no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×D8—22no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#214—41no—
124C3×#213—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×C4×Dic3—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3297—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#237C22×C311yescharacteristic
148C2×D3×D4C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—21no—
151C2×C3×D8—31no—
152C2×C3×D8C2×D311yescharacteristic
153C2×C3×D8C22×C311yescharacteristic
154C22×C3×C8—31no—
155C22×C3×C8—31no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#124—31no—
159C3×#123—61no—
160C3×#123—61no—
161C3×C22⋊Q8—31no—
162C3×#121—31no—
163C3×#121—31no—
164C3×#121—31no—
165C3×#121—61no—
166C3×#121—61no—
167C3×#120—61no—
168C3×C4×D4—21no—
169C3×C4×D4—21no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4C2×D311yescharacteristic
173C3×C4×D4C2×D311yescharacteristic, complemented
174C3×C4×D4C22×C311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic, complemented
176C3×#117—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—61no—
179#938C22×C311yescharacteristic
180#938C22×C311yescharacteristic, complemented
181C2×#214C22×C311yescharacteristic, complemented
182C2×#213C22×C311yescharacteristic
183#930—21no—
184#929—21no—
185C4×#67—21no—
186C2×(C2×D3)⋊C4—21no—
187C2×D3×C8C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic, complemented
189#897C22×C311yescharacteristic
190#895C22×C311yescharacteristic
191#892C22×C311yescharacteristic, complemented
192D3×C4⋊C4C22×C311yescharacteristic
193#886—21no—
194#884—21no—
195#882—21no—
196#879—21no—
197#875C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic
199#870C22×C311yescharacteristic, complemented
200C3×#107—21no—
201C3×#107—31no—
202C3×#107C2×D311yescharacteristic, complemented
203C3×#107C22×C311yescharacteristic, complemented
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102C2×D311yescharacteristic
217C3×#102C2×D311yescharacteristic, complemented
218C3×#102C22×C311yescharacteristic
219C3×#102C22×C311yescharacteristic, complemented
220C3×C22⋊C8—31no—
221C3×C22⋊C8—31no—
222C3×C4×C8—21no—
223C3×C4×C8C2×D311yescharacteristic, complemented
224C3×C4×C8C22×C311yescharacteristic, complemented
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic, complemented
231#816C22×C311yescharacteristic, complemented
232#816C22×C311yescharacteristic, complemented
233#810C22×C311yescharacteristic, complemented
234#809C22×C311yescharacteristic
235#808C22×C311yescharacteristic, complemented
236#807C22×C311yescharacteristic, complemented
237C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
253C2×C32×C4—81no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—42no—
258C3×#67—42no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—22no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—81no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—31no—
284#488—31no—
285#484—31no—
286#482—31no—
287#478—31no—
288#466—31no—
289#465—31no—
290#463—31no—
291#449—31no—
292#447—31no—
293C4×D8C3×D311yescharacteristic, complemented
294C8×D4—31no—
295#416—31no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C23×C311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—41no—
324C22×C3×C4—41no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—21no—
331C22×Dic3—21no—
332#237—22no—
333#237—41no—
334D3×D4—22no—
335D3×D4—41no—
336C2×D12—21no—
337C2×D12C3×D411yescharacteristic
338C2×D12C23×C311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3C23×C311yescharacteristic
341C2×C4×D3C23×C311yescharacteristic
342C2×Dic6C23×C311yescharacteristic
343C3×SD16—121no—
344C3×D8—24no—
345C3×D8—22no—
346C3×D8—22no—
347C3×D8—121no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C23×C311yescharacteristic
357C2×C3×C8C23×C311yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C4⋊C4C23×C311yescharacteristic
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C42—21no—
387C3×C42—61no—
388C3×C42C22×D311yescharacteristic
389C3×C42C23×C311yescharacteristic
390#217—21no—
391#217—21no—
392#214—41no—
393#213—41no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4C3×D411yescharacteristic
400(C2×D3)⋊C4C3×D411yescharacteristic
401C4⋊Dic3—21no—
402C4⋊Dic3C3×D411yescharacteristic
403C4⋊Dic3C23×C311yescharacteristic
404C4⋊Dic3C23×C311yescharacteristic
405Dic3⋊C4—21no—
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408C4×Dic3—21no—
409C2×C3⋊C8C23×C311yescharacteristic
410C2×C3⋊C8C23×C311yescharacteristic
411D3×C8—41no—
412D3×C8—41no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C2×C3×D3#13512yes—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×D4—31no—
443C2×SD16—31no—
444C2×D8—31no—
445C2×D8C2×C3×D311yescharacteristic
446C22×C8—31no—
447C22×C8—31no—
448#126—61no—
449#125—31no—
450#124—31no—
451#123—61no—
452#123—61no—
453C22⋊Q8—31no—
454#121—31no—
455#121—31no—
456#121—31no—
457#121—61no—
458#121—61no—
459#120—61no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4C2×C3×D311yescharacteristic
463C4×D4C2×C3×D311yescharacteristic, complemented
464#117—31no—
465C2×C4⋊C4—31no—
466C2×C22⋊C4—61no—
467#107—31no—
468#107C2×C3×D311yescharacteristic, complemented
469#106—31no—
470C4⋊C8—31no—
471#103—31no—
472#103—31no—
473#103—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102C2×C3×D311yescharacteristic
480#102C2×C3×D311yescharacteristic, complemented
481C22⋊C8—31no—
482C22⋊C8—31no—
483C4×C8C2×C3×D311yescharacteristic, complemented
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C22×D3—21no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—81no—
500C22×D3C2×C3×D411yescharacteristic
501C22×D3C2×C3×D411yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—22no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—62no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—122no—
518C3×D4—122no—
519C3×D4—122no—
520C3×D4—241no—
521C3×D4—241no—
522C3×D4#23512yes—
523C3×D4C3×#4112yes—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—81no—
543C2×C3×C4—81no—
544C2×C3×C4—81no—
545C2×C3×C4—81no—
546C2×C3×C4—82no—
547C2×C3×C4—82no—
548C2×C3×C4—122no—
549C2×C3×C4—241no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C2×C3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C24×C311yescharacteristic
556#67—42no—
557#67—42no—
558#67—42no—
559#67—81no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—42no—
564C2×Dic3C2×C3×D411yescharacteristic
565C2×Dic3C2×C3×D411yescharacteristic
566D12—22no—
567D12—21no—
568D12—21no—
569D12—81no—
570C4×D3—21no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—21no—
574C4×D3—81no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—22no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32—42no—
588C2×C32—81no—
589C2×C32#54611yescharacteristic
590C2×C32C2×#13511yescharacteristic
591C2×C32#57611yescharacteristic
592C3×D3—22no—
593C3×D3—41no—
594C3×D3—81no—
595C24—61no—
596#41—62no—
597#41—121no—
598C2×Q8—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—121no—
608C2×D4C22×C3×D311yescharacteristic
609C2×D4C22×C3×D311yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—61no—
616SD16—121no—
617D8—22no—
618D8—121no—
619C2×C8—31no—
620C2×C8—31no—
621C2×C8—121no—
622C2×C8—121no—
623C2×C8C22×C3×D311yescharacteristic
624C2×C8C22×C3×D311yescharacteristic
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4C22×C3×D311yescharacteristic
633C4⋊C4C22×C3×D311yescharacteristic
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C42—61no—
646C42C22×C3×D311yescharacteristic
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—21no—
650C22×C3—32no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3C2×D3×D411yescharacteristic
677C22×C3C22×C3×D411yescharacteristic
678C2×D3—21no—
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—84no—
687C2×D3C3×#13512yes—
688C3×C4—22no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—81no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4C2×#23511yescharacteristic
708C3×C4#100911yescharacteristic
709C3×C4C2×C3×#4111yescharacteristic
710C3×C4C3×H(5,𝔽2)11yescharacteristic
711Dic3—21no—
712Dic3—21no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716C32#329711yescharacteristic, complemented, Sylow
717C23—21no—
718C23—21no—
719C23—31no—
720C23—31no—
721C23—61no—
722C23—122no—
723C23—122no—
724C23—241no—
725Q8—61no—
726Q8—61no—
727D4—21no—
728D4—21no—
729D4—21no—
730D4—62no—
731D4—61no—
732D4—61no—
733D4—122no—
734D4—122no—
735D4—122no—
736D4—241no—
737D4—241no—
738D4C3×#23512yes—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—122no—
753C2×C4—241no—
754C2×C4C3×D3×D411yescharacteristic
755C2×C4C3×D3×D411yescharacteristic
756C2×C4C23×C3×D311yescharacteristic
757C8—21no—
758C8—21no—
759C8—61no—
760C8—61no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—62no—
767C2×C3—82no—
768C2×C3—82no—
769C2×C3—81no—
770C2×C3—81no—
771C2×C3—121no—
772C2×C3—241no—
773C2×C3#555011yescharacteristic
774C2×C3#575711yescharacteristic
775C2×C3D3×#13511yescharacteristic
776C2×C3C3×#54611yescharacteristic
777C2×C3C2×C3×#13511yescharacteristic
778C2×C3C3×#57611yescharacteristic
779D3—22no—
780D3—41no—
781D3—81no—
782C22—22no—
783C22—32no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—244no—
798C22C2×C3×D3×D411yescharacteristic
799C4—21no—
800C4—21no—
801C4—41no—
802C4—41no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4C2×C3×#23511yescharacteristic
809C4C3×#100911yescharacteristic
810C3—21no—
811C3#7960911yescharacteristic, direct product factor
812C3C3×#329711yescharacteristic, complemented
813C2—42no—
814C2—62no—
815C2—81no—
816C2—121no—
817C2—241no—
818C2C3×#555011yescharacteristic
819C2C3×#575711yescharacteristic
820C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC3×C4×D8D3
hypocenterC3C3×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5558C2semidirect
2. C3×#5554C2semidirect
3. C32×C4×D8C2semidirect
4. C3×#5158C2semidirect
5. C3×#5156C2semidirect
6. C3×#5016C2semidirect
7. C3×#5009C2semidirect
8. C3×#4885C2semidirect
9. C3×#4884C2semidirect
10. C3×#4778C2semidirect
11. C3×#4775C2semidirect
12. C3×#4772C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4697C2semidirect
15. C3×C8×D12C2semidirect
17. #79609C3direct (N × H)
22. C32×C4×D4C22semidirect
24. C3×#938C22semidirect
25. C2×C3×#214C22semidirect
32. C2×C3×D3×C8C22semidirect
35. C3×#892C22semidirect
43. C3×#870C22semidirect
44. C32×#107C22semidirect
46. C32×#102C22semidirect
47. C32×C4×C8C22semidirect
53. C3×(C2×D3)⋊C8C22semidirect
54. C3×#816C22semidirect
55. C3×#816C22semidirect
56. C3×#810C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5558C2×C3semidirect
64. #5554C2×C3semidirect
75. C3×C4×D8D3semidirect
76. C3×C4×D8C2×C3semidirect
80. #5158C2×C3semidirect
81. #5156C2×C3semidirect
82. #5016C2×C3semidirect
83. #5009C2×C3semidirect
84. #4885C2×C3semidirect
85. #4884C2×C3semidirect
86. #4778C2×C3semidirect
87. #4775C2×C3semidirect
88. #4772C2×C3semidirect
89. D3×#102C2×C3semidirect
90. #4697C2×C3semidirect
91. C8×D12C2×C3semidirect
173. C3×C4×D4C2×D3semidirect
175. C3×C4×D4C22×C3semidirect
180. #938C22×C3semidirect
181. C2×#214C22×C3semidirect
188. C2×D3×C8C22×C3semidirect
191. #892C22×C3semidirect
199. #870C22×C3semidirect
202. C3×#107C2×D3semidirect
203. C3×#107C22×C3semidirect
217. C3×#102C2×D3semidirect
219. C3×#102C22×C3semidirect
223. C3×C4×C8C2×D3semidirect
224. C3×C4×C8C22×C3semidirect
230. (C2×D3)⋊C8C22×C3semidirect
231. #816C22×C3semidirect
232. #816C22×C3semidirect
233. #810C22×C3semidirect
235. #808C22×C3semidirect
236. #807C22×C3semidirect
237. C4⋊(C3⋊C8)C22×C3semidirect
293. C4×D8C3×D3semidirect
463. C4×D4C2×C3×D3semidirect
468. #107C2×C3×D3semidirect
480. #102C2×C3×D3semidirect
483. C4×C8C2×C3×D3semidirect
716. C32#3297semidirect
811. C3#79609direct (N × H)
812. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#55582
C3×#55542
C32×C4×D82
C3×#51582
C3×#51562
C3×#50162
C3×#50092
C3×#48852
C3×#48842
C3×#47782
C3×#47752
C3×#47722
C3×D3×#1022
C3×#46972
C3×C8×D122
C3×#32973
#796093