Finite Group Databasebeta

← C3×#79803 #11889823

Subgroups — C3×#79803 #11889823

Order 1152.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5581C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5173C211yesmaximal, characteristic, complemented
5C3×#5173C211yesmaximal, characteristic, complemented
6C3×#5031C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4888C211yesmaximal, characteristic, complemented
9C3×#4884C211yesmaximal, characteristic, complemented
10C3×#4816C211yesmaximal, characteristic, complemented
11C3×#4813C211yesmaximal, characteristic, complemented
12C3×#4772C211yesmaximal, characteristic, complemented
13C3×#4771C211yesmaximal, characteristic, complemented
14C3×#4706C211yesmaximal, characteristic, complemented
15C3×#4703C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#79803C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#930—21no—
28C2×C3×C4⋊Dic3—21no—
29C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#894—21no—
34C3×#892C2211yescharacteristic
35C3×D3×C4⋊C4C2211yescharacteristic
36C3×#889—21no—
37C3×#886—21no—
38C3×#886—21no—
39C3×#876—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872—21no—
42C3×#870C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#97C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#552—31no—
62C3×#547—31no—
63#5581C2×C311yescharacteristic, complemented
64#5555C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#484—31no—
68C3×#478—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#452—31no—
73C3×#452—31no—
74C3×#440—21no—
75C3×#440D311yescharacteristic, complemented
76C3×#440C2×C311yescharacteristic, complemented
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5173C2×C311yescharacteristic, complemented
81#5173C2×C311yescharacteristic, complemented
82#5031C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4888C2×C311yescharacteristic, complemented
85#4884C2×C311yescharacteristic, complemented
86#4816C2×C311yescharacteristic, complemented
87#4813C2×C311yescharacteristic, complemented
88#4772C2×C311yescharacteristic, complemented
89#4771C2×C311yescharacteristic, complemented
90#4706C2×C311yescharacteristic, complemented
91#4703C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C3×#237—41no—
102C3×#237—41no—
103C2×C3×D12D411yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C32×SD16—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C3×#216—41no—
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
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×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3315—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C22×C311yescharacteristic
148C2×#237C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—21no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C22×C311yescharacteristic
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×#126—61no—
158C3×#125—31no—
159C3×#125—61no—
160C3×#123—61no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—61no—
168C3×C4×Q8—21no—
169C3×C4×Q8C2×D311yescharacteristic
170C3×C4×Q8C22×C311yescharacteristic
171C3×C4×D4—21no—
172C3×C4×D4—31no—
173C3×C4×D4C2×D311yescharacteristic
174C3×C4×D4C22×C311yescharacteristic
175C3×#117—31no—
176C3×#117—61no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—61no—
179#946C22×C311yescharacteristic
180#946C22×C311yescharacteristic
181C2×#216C22×C311yescharacteristic
182C2×#216C22×C311yescharacteristic
183#930—21no—
184C2×C4⋊Dic3—21no—
185C2×ΓL(1,𝔽25)C22×C311yescharacteristic
186C2×D3×C8C22×C311yescharacteristic
187#897C22×C311yescharacteristic
188#897C22×C311yescharacteristic
189#894—21no—
190#892C22×C311yescharacteristic
191D3×C4⋊C4C22×C311yescharacteristic
192#889—21no—
193#886—21no—
194#886—21no—
195#876—21no—
196C4×D12C22×C311yescharacteristic
197#872—21no—
198#870C22×C311yescharacteristic
199#869C22×C311yescharacteristic
200C3×#107—21no—
201C3×#107—31no—
202C3×#107C2×D311yescharacteristic
203C3×#107C22×C311yescharacteristic
204C3×#106—31no—
205C3×C4⋊C8—31no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#102—21no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×C22⋊C8—31no—
221C3×C22⋊C8—31no—
222C3×#97—21no—
223C3×#97C2×D311yescharacteristic
224C3×#97C22×C311yescharacteristic
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#808C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237C4⋊(C3⋊C8)C22×C311yescharacteristic
238C23×C32—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—41no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#547—31no—
278#491—31no—
279#485—31no—
280#484—31no—
281#478—31no—
282#470—31no—
283#467—31no—
284#462—31no—
285#452—31no—
286#452—31no—
287#440C3×D311yescharacteristic, complemented
288#435—31no—
289#417—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—121no—
294C3×#41—121no—
295C2×C3×Q8—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C23×C311yescharacteristic
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C2×#67—21no—
315C2×#67—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318#237—22no—
319#237—22no—
320#237—41no—
321#237—41no—
322C2×D12C3×D411yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3C23×C311yescharacteristic
325C2×C4×D3C23×C311yescharacteristic
326C2×Dic6C23×C311yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—121no—
329C3×Q16—121no—
330C3×SD16—24no—
331C3×SD16—22no—
332C3×SD16—22no—
333C3×M16—121no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—41no—
378C3×C42—61no—
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381#216—41no—
382#216—41no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4C3×D411yescharacteristic
389(C2×D3)⋊C4C3×D411yescharacteristic
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C3×D411yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396C4⋊Dic3C23×C311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C2×C3⋊C8C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405ΓL(1,𝔽25)—41no—
406D3×C8—41no—
407C22×C32—22no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C2×#41—31no—
431C2×#41—31no—
432C2×Q16—31no—
433C2×Q16—31no—
434C2×SD16C2×C3×D311yescharacteristic
435C2×M16—31no—
436C22×C8—31no—
437C4⋊Q8—31no—
438#126—61no—
439#125—31no—
440#125—61no—
441#123—61no—
442#123—61no—
443#123—61no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448#121—61no—
449C4×Q8C2×C3×D311yescharacteristic
450C4×D4—31no—
451C4×D4C2×C3×D311yescharacteristic
452#117—31no—
453#117—61no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—61no—
456#107—31no—
457#107C2×C3×D311yescharacteristic
458#106—31no—
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103C2×C3×D311yescharacteristic
467#102—31no—
468#102—31no—
469#102C2×C3×D311yescharacteristic
470C22⋊C8—31no—
471C22⋊C8—31no—
472#97C2×C3×D311yescharacteristic
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—31no—
477C23×C3—41no—
478C22×D3C2×C3×D411yescharacteristic
479C22×D3C2×C3×D411yescharacteristic
480C3×Q8—22no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—41no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—61no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4—121no—
495C3×D4—122no—
496C3×D4—122no—
497C3×D4#23512yes—
498C3×D4C3×#4112yes—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—82no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—42no—
534#67—42no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543D12—41no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—21no—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—42no—
564C2×C32#54611yescharacteristic
565C2×C32#57511yescharacteristic
566C2×C32#57811yescharacteristic
567C3×D3—41no—
568C3×D3—41no—
569#41—62no—
570#41—62no—
571#41—121no—
572#41—121no—
573C2×Q8—31no—
574C2×Q8—31no—
575C2×Q8C22×C3×D311yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C22×C3×D311yescharacteristic
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586Q16—121no—
587Q16—121no—
588SD16—22no—
589M16—121no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—121no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4C22×C3×D311yescharacteristic
609C4⋊C4C22×C3×D311yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C42—21no—
619C42—61no—
620C42C22×C3×D311yescharacteristic
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C22×C3×D411yescharacteristic
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4#100911yescharacteristic
670C3×C4C2×C3×#4111yescharacteristic
671C3×C4C3×H(5,𝔽2)11yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678C32#331511yescharacteristic, complemented, Sylow
679C23—21no—
680C23—31no—
681C23—31no—
682Q8—21no—
683Q8—21no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—61no—
688D4—21no—
689D4—121no—
690D4—122no—
691D4—122no—
692D4C3×#23512yes—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—42no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4C3×D3×D411yescharacteristic
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C23×C3×D311yescharacteristic
713C8—21no—
714C8—21no—
715C8—61no—
716C8—61no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—121no—
724C2×C3—121no—
725C2×C3#555011yescharacteristic
726C2×C3#577311yescharacteristic
727C2×C3#577911yescharacteristic
728C2×C3C3×#54611yescharacteristic
729C2×C3C3×#57511yescharacteristic
730C2×C3C3×#57811yescharacteristic
731D3—41no—
732D3—41no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22C2×C3×D3×D411yescharacteristic
743C4—21no—
744C4—21no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—61no—
749C4—61no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4C2×C3×#23511yescharacteristic
755C4C3×#100911yescharacteristic
756C3—21no—
757C3#7980311yescharacteristic, direct product factor
758C3C3×#331511yescharacteristic, complemented
759C2—42no—
760C2—121no—
761C2—121no—
762C2C3×#555011yescharacteristic
763C2C3×#577311yescharacteristic
764C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC3×#440D3
hypocenterC3C3×#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5581C2semidirect
3. C32×#440C2semidirect
4. C3×#5173C2semidirect
5. C3×#5173C2semidirect
6. C3×#5031C2semidirect
7. C3×#5009C2semidirect
8. C3×#4888C2semidirect
9. C3×#4884C2semidirect
10. C3×#4816C2semidirect
11. C3×#4813C2semidirect
12. C3×#4772C2semidirect
13. C3×#4771C2semidirect
14. C3×#4706C2semidirect
15. C3×#4703C2semidirect
17. #79803C3direct (N × H)
63. #5581C2×C3semidirect
75. C3×#440D3semidirect
76. C3×#440C2×C3semidirect
80. #5173C2×C3semidirect
81. #5173C2×C3semidirect
82. #5031C2×C3semidirect
83. #5009C2×C3semidirect
84. #4888C2×C3semidirect
85. #4884C2×C3semidirect
86. #4816C2×C3semidirect
87. #4813C2×C3semidirect
88. #4772C2×C3semidirect
89. #4771C2×C3semidirect
90. #4706C2×C3semidirect
91. #4703C2×C3semidirect
287. #440C3×D3semidirect
678. C32#3315semidirect
757. C3#79803direct (N × H)
758. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C3×#55812
C3×#55552
C32×#4402
C3×#51732
C3×#50312
C3×#50092
C3×#48882
C3×#48842
C3×#48162
C3×#48132
C3×#47722
C3×#47712
C3×#47062
C3×#47032
C3×#33153
#798033