Finite Group Databasebeta

← C3×#79873 #11872268

Subgroups — C3×#79873 #11872268

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5562C211yesmaximal, characteristic, complemented
2C3×#5546C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6C3×C4×#214C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4857C211yesmaximal, characteristic, complemented
10C3×#4781C211yesmaximal, characteristic, complemented
11C3×#4774C211yesmaximal, characteristic, complemented
12C3×#4766C211yesmaximal, characteristic, complemented
13C3×#4762C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4709C211yesmaximal, characteristic, complemented
16C3×#3119—31nomaximal
17#79873C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C3×#929—21no—
29C3×C4×#67—21no—
30C2×C3×Dic3⋊C4—21no—
31C2×C3×#204C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#890C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#884—21no—
37C3×#883—21no—
38C3×#67⋊C4—21no—
39C3×#877—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#540—31no—
62C3×#520—31no—
63#5562C2×C311yescharacteristic, complemented
64#5546C2×C311yescharacteristic, complemented
65C3×#481—31no—
66C3×#480—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#460—31no—
70C3×#459—31no—
71C3×#449—31no—
72C3×#449—31no—
73C3×#442—21no—
74C3×#442D311yescharacteristic, complemented
75C3×#442C2×C311yescharacteristic, complemented
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5158C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic, complemented
82C4×#214C2×C311yescharacteristic, complemented
83C4×#213C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4857C2×C311yescharacteristic, complemented
86#4781C2×C311yescharacteristic, complemented
87#4774C2×C311yescharacteristic, complemented
88#4766C2×C311yescharacteristic, complemented
89#4762C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4709C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—22no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C32×D8—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141#3119—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×D8—21no—
147C2×C3×D8—31no—
148C2×C3×D8C2×D311yescharacteristic
149C2×C3×D8C22×C311yescharacteristic
150C3×#127—31no—
151C3×#125—31no—
152C3×#123—61no—
153C3×#123—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—21no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C22×C311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—31no—
171C3×#117—61no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—61no—
174#940C22×C311yescharacteristic
175#938C22×C311yescharacteristic
176D4×Dic3C22×C311yescharacteristic
177C2×#214C22×C311yescharacteristic
178C2×#213C22×C311yescharacteristic
179#930—21no—
180#929—21no—
181C4×#67—21no—
182C2×Dic3⋊C4—21no—
183C2×#204C22×C311yescharacteristic
184#895C22×C311yescharacteristic
185D3×C4⋊C4C22×C311yescharacteristic
186#890C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#884—21no—
189#883—21no—
190#67⋊C4—21no—
191#877—21no—
192C4×D12C22×C311yescharacteristic
193#872C22×C311yescharacteristic
194C4×Dic6C22×C311yescharacteristic
195C3×#107—31no—
196C3×#107—31no—
197C3×#106—21no—
198C3×#106—31no—
199C3×#106C2×D311yescharacteristic
200C3×#106C22×C311yescharacteristic
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—21no—
206C3×#102—21no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×C22⋊C8—31no—
216C3×C22⋊C8—31no—
217C3×#97—21no—
218C3×#97C2×D311yescharacteristic
219C3×#97C22×C311yescharacteristic
220C3×C4×C8—31no—
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#816C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229Dic3⋊C8C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4×C3⋊C8C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—81no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—24no—
251C3×#67—81no—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—81no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6#4112yes—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—31no—
276#520—31no—
277#481—31no—
278#480—31no—
279#479—31no—
280#478—31no—
281#460—31no—
282#459—31no—
283#449—31no—
284#449—31no—
285#442C3×D311yescharacteristic, complemented
286#440—31no—
287C4×SD16—31no—
288C4×D8—31no—
289#433—31no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C2×C3×D4C23×C311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—41no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322#237—22no—
323#237—22no—
324C2×D12—21no—
325C2×D12C23×C311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3C23×C311yescharacteristic
329C2×Dic6C23×C311yescharacteristic
330C3×SD16—62no—
331C3×SD16—62no—
332C3×D8—24no—
333C3×D8—22no—
334C3×D8—22no—
335C3×D8—62no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—41no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—31no—
373C3×C42—61no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C23×C311yescharacteristic
377#217—21no—
378#217—21no—
379#214—22no—
380#213—22no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4C3×D411yescharacteristic
384(C2×D3)⋊C4C3×D411yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3C23×C311yescharacteristic
387C4⋊Dic3C23×C311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4C3×D411yescharacteristic
393Dic3⋊C4C3×D411yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399#204—22no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—31no—
426C2×SD16—31no—
427C2×SD16—31no—
428C2×D8—31no—
429C2×D8C2×C3×D311yescharacteristic
430#127—31no—
431#125—31no—
432#123—61no—
433#123—61no—
434#121—31no—
435#121—31no—
436#121—61no—
437#121—61no—
438C4×Q8—31no—
439C4×Q8—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4C2×C3×D311yescharacteristic
445C4×D4C2×C3×D311yescharacteristic
446#117—31no—
447#117—61no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—61no—
450#107—31no—
451#107—31no—
452#106—31no—
453#106C2×C3×D311yescharacteristic
454C4⋊C8—31no—
455C4⋊C8—31no—
456#103—31no—
457#103—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102C2×C3×D311yescharacteristic
463#102C2×C3×D311yescharacteristic
464C22⋊C8—31no—
465C22⋊C8—31no—
466#97C2×C3×D311yescharacteristic
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—61no—
476C22×D3—21no—
477C22×D3C2×C3×D411yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×D4—22no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—241no—
494C3×D4—241no—
495C3×D4—241no—
496C3×D4—241no—
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—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—64no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—81no—
520C2×C3×C4—81no—
521C2×C3×C4—82no—
522C2×C3×C4—82no—
523C2×C3×C4—241no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C24×C311yescharacteristic
532#67—24no—
533#67—81no—
534#67—81no—
535#67—81no—
536C2×Dic3—24no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—81no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—81no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—81no—
550C4×D3—81no—
551Dic6—21no—
552Dic6C3×#4112yes—
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—81no—
565C2×C32#52511yescharacteristic
566C2×C32#57611yescharacteristic
567C2×C32#57711yescharacteristic
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C22×C3×D311yescharacteristic
580C2×D4C22×C3×D311yescharacteristic
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588SD16—62no—
589SD16—62no—
590D8—22no—
591D8—62no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4C22×C3×D311yescharacteristic
606C4⋊C4C22×C3×D311yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C42—31no—
616C42—61no—
617C42—61no—
618C42C22×C3×D311yescharacteristic
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×C3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—62no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23511yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675C3×C4C2×C3×#4111yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—22no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682C32#311911yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—31no—
686C23—61no—
687Q8—32no—
688Q8—61no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—64no—
693D4—61no—
694D4—61no—
695D4—241no—
696D4—241no—
697D4—241no—
698D4—241no—
699D4C3×#23512yes—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—64no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4C3×D3×D411yescharacteristic
717C2×C4C3×D3×D411yescharacteristic
718C2×C4C23×C3×D311yescharacteristic
719C8—21no—
720C8—21no—
721C8—61no—
722C8—61no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—82no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—121no—
733C2×C3—241no—
734C2×C3#554711yescharacteristic
735C2×C3#577411yescharacteristic
736C2×C3#577511yescharacteristic
737C2×C3C3×#52511yescharacteristic
738C2×C3C3×#57611yescharacteristic
739C2×C3C3×#57711yescharacteristic
740D3—41no—
741D3—81no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22C2×C3×D3×D411yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—62no—
763C4—121no—
764C4—121no—
765C4C2×C3×#23511yescharacteristic
766C4C3×D3×#4111yescharacteristic
767C3—21no—
768C3#7987311yescharacteristic, direct product factor
769C3C3×#311911yescharacteristic, complemented
770C2—42no—
771C2—81no—
772C2—121no—
773C2—241no—
774C2C3×#554711yescharacteristic
775C2C3×#577411yescharacteristic
776C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenterC3×#442D3
hypocenterC3C3×#3119
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
1. C3×#5562C2semidirect
2. C3×#5546C2semidirect
3. C32×#442C2semidirect
4. C3×#5158C2semidirect
5. C3×#5150C2semidirect
6. C3×C4×#214C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4863C2semidirect
9. C3×#4857C2semidirect
10. C3×#4781C2semidirect
11. C3×#4774C2semidirect
12. C3×#4766C2semidirect
13. C3×#4762C2semidirect
14. C3×#4710C2semidirect
15. C3×#4709C2semidirect
17. #79873C3direct (N × H)
63. #5562C2×C3semidirect
64. #5546C2×C3semidirect
74. C3×#442D3semidirect
75. C3×#442C2×C3semidirect
80. #5158C2×C3semidirect
81. #5150C2×C3semidirect
82. C4×#214C2×C3semidirect
83. C4×#213C2×C3semidirect
84. #4863C2×C3semidirect
85. #4857C2×C3semidirect
86. #4781C2×C3semidirect
87. #4774C2×C3semidirect
88. #4766C2×C3semidirect
89. #4762C2×C3semidirect
90. #4710C2×C3semidirect
91. #4709C2×C3semidirect
285. #442C3×D3semidirect
682. C32#3119semidirect
768. C3#79873direct (N × H)
769. C3C3×#3119semidirect

Maximal subgroups

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

subgroupindex
C3×#55622
C3×#55462
C32×#4422
C3×#51582
C3×#51502
C3×C4×#2142
C3×C4×#2132
C3×#48632
C3×#48572
C3×#47812
C3×#47742
C3×#47662
C3×#47622
C3×#47102
C3×#47092
C3×#31193
#798733