Finite Group Databasebeta

← C3×#81655 #11887861

Subgroups — C3×#81655 #11887861

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5695C211yesmaximal, characteristic, complemented
2C3×#5677C211yesmaximal, characteristic, complemented
3C32×#488C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5057C211yesmaximal, characteristic, complemented
6C3×#4815C211yesmaximal, characteristic, complemented
7C3×#4807C211yesmaximal, characteristic, complemented
8C3×#4806C211yesmaximal, characteristic, complemented
9C3×D3×#103C211yesmaximal, characteristic, complemented
10C3×#4781C211yesmaximal, characteristic, complemented
11C3×#4777C211yesmaximal, characteristic, complemented
12C3×#4775C211yesmaximal, characteristic, complemented
13C3×#4772C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×C8×D12C211yesmaximal, characteristic, complemented
16C3×#3301—31nomaximal
17#81655C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#898—21no—
30C3×#895—21no—
31C3×#895C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#894—21no—
34C3×#893—21no—
35C3×#892C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#885—21no—
38C3×#884—21no—
39C3×#67⋊C4—21no—
40C3×#878—21no—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#553—31no—
62C3×#548—31no—
63#5695C2×C311yescharacteristic, complemented
64#5677C2×C311yescharacteristic, complemented
65C3×#488—21no—
66C3×#488D311yescharacteristic, complemented
67C3×#488C2×C311yescharacteristic, complemented
68C3×#485—31no—
69C3×#481—31no—
70C3×#479—31no—
71C3×#466—31no—
72C3×#465—31no—
73C3×#463—31no—
74C3×#449—31no—
75C3×#448—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#103—31no—
80#5063C2×C311yescharacteristic, complemented
81#5057C2×C311yescharacteristic, complemented
82#4815C2×C311yescharacteristic, complemented
83#4807C2×C311yescharacteristic, complemented
84#4806C2×C311yescharacteristic, complemented
85D3×#103C2×C311yescharacteristic, complemented
86#4781C2×C311yescharacteristic, complemented
87#4777C2×C311yescharacteristic, complemented
88#4775C2×C311yescharacteristic, complemented
89#4772C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91C8×D12C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×Q8—22no—
98C3×D3×Q8—41no—
99C3×#237—22no—
100C3×#237—41no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#215—41no—
123C3×#213—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142C3×D3×C8—41no—
143C3×D3×C8—41no—
144#3301—31noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C2×#237C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—21no—
156C3×#125C2×D311yescharacteristic
157C3×#125C22×C311yescharacteristic
158C3×#124—21no—
159C3×#124—61no—
160C3×#124C2×D311yescharacteristic
161C3×#124C22×C311yescharacteristic
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—61no—
165C3×#121—31no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×C4×D4—61no—
175C3×#117—31no—
176C2×C3×C4⋊C4—31no—
177#946C22×C311yescharacteristic
178C2×#215C22×C311yescharacteristic
179#938C22×C311yescharacteristic
180C2×#213C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182C2×D3×C8C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#895—21no—
186#895C22×C311yescharacteristic
187#895C22×C311yescharacteristic
188#894—21no—
189#893—21no—
190#892C22×C311yescharacteristic
191D3×C4⋊C4C22×C311yescharacteristic
192#885—21no—
193#884—21no—
194#67⋊C4—21no—
195#878—21no—
196C4×D12C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C3×#107—31no—
200C3×#106—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C2×D311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#102—21no—
214C3×#102—21no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—21no—
224C3×C4×C8C2×D311yescharacteristic
225C3×C4×C8C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230(C2×D3)⋊C8C22×C311yescharacteristic
231#817C22×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×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
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—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—22no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—42no—
264C3×D12—81no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—42no—
274C3×Dic6#4112yes—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#548—31no—
281#488C3×D311yescharacteristic, complemented
282#485—31no—
283#481—31no—
284#479—31no—
285#466—31no—
286#465—31no—
287#463—31no—
288#449—31no—
289#448—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#103—31no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C23×C311yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C2×#67—21no—
319C2×#67—21no—
320C22×Dic3—21no—
321D3×Q8—22no—
322D3×Q8—41no—
323#237—22no—
324#237—41no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12C3×D411yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C2×C4×D3C23×C311yescharacteristic
334C2×Dic6—21no—
335C2×Dic6C23×C311yescharacteristic
336C3×SD16—62no—
337C3×SD16—121no—
338C3×D8—121no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—121no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C23×C311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—31no—
373C3×C22⋊C4—41no—
374C3×C22⋊C4—41no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—21no—
382C3×C42—61no—
383C3×C42—61no—
384C3×C42C22×D311yescharacteristic
385C3×C42C23×C311yescharacteristic
386#217—21no—
387#215—41no—
388#213—41no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4C3×D411yescharacteristic
395(C2×D3)⋊C4C3×D411yescharacteristic
396C4⋊Dic3C3×D411yescharacteristic
397C4⋊Dic3C23×C311yescharacteristic
398C4⋊Dic3C23×C311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406#204—22no—
407D3×C8—41no—
408D3×C8—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3×Dic3—22no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C2×#41—31no—
435C22×Q8—31no—
436C2×SD16—31no—
437C2×SD16—31no—
438C2×D8—31no—
439C22×C8—31no—
440C22×C8—31no—
441#126—61no—
442#125C2×C3×D311yescharacteristic
443#124—61no—
444#124C2×C3×D311yescharacteristic
445#123—61no—
446C22⋊Q8—31no—
447C22⋊Q8—61no—
448#121—31no—
449#121—31no—
450#121—31no—
451#121—61no—
452#121—61no—
453C4×Q8—31no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—61no—
457C4×D4—61no—
458#117—31no—
459C2×C4⋊C4—31no—
460#107—31no—
461#106—31no—
462#106—31no—
463C4⋊C8—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102—31no—
472#102C2×C3×D311yescharacteristic
473#102C2×C3×D311yescharacteristic
474C22⋊C8—31no—
475C22⋊C8—31no—
476C4×C8C2×C3×D311yescharacteristic
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—41no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3C2×C3×D411yescharacteristic
485C22×D3C2×C3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8—122no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4—122no—
506C3×D4—122no—
507C3×D4—241no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—122no—
530C2×C3×C4—122no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—42no—
540#67—42no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—42no—
545C2×Dic3C2×C3×D411yescharacteristic
546C2×Dic3C2×C3×D411yescharacteristic
547D12—22no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12—81no—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—81no—
558C4×D3—81no—
559Dic6—21no—
560Dic6—42no—
561Dic6C3×#4112yes—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—81no—
573C2×C32#54611yescharacteristic
574C2×C32C2×#13511yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C3×D3—41no—
578C3×D3—81no—
579#41—62no—
580#41—121no—
581C2×Q8—31no—
582C2×Q8—61no—
583C2×Q8—62no—
584C2×Q8—121no—
585C2×Q8C22×C3×D311yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4C22×C3×D311yescharacteristic
593C22×C4—31no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599SD16—62no—
600SD16—121no—
601D8—121no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—121no—
605C2×C8—121no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C42—61no—
629C42—61no—
630C42C22×C3×D311yescharacteristic
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×C3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3C3×#13512yes—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—62no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685C3×C4C2×C3×#4111yescharacteristic
686C3×C4C3×H(5,𝔽2)11yescharacteristic
687Dic3—22no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692C32#330111yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—31no—
696C23—61no—
697Q8—21no—
698Q8—21no—
699Q8—32no—
700Q8—61no—
701Q8—122no—
702D4—21no—
703D4—21no—
704D4—62no—
705D4—61no—
706D4—61no—
707D4—122no—
708D4—122no—
709D4—122no—
710D4—241no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—241no—
726C2×C4—241no—
727C2×C4C3×D3×D411yescharacteristic
728C2×C4C3×D3×D411yescharacteristic
729C2×C4C23×C3×D311yescharacteristic
730C8—21no—
731C8—21no—
732C8—61no—
733C8—61no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—62no—
738C2×C3—81no—
739C2×C3—81no—
740C2×C3—121no—
741C2×C3—161no—
742C2×C3—241no—
743C2×C3#567611yescharacteristic
744C2×C3D3×#13511yescharacteristic
745C2×C3#577011yescharacteristic
746C2×C3C3×#54611yescharacteristic
747C2×C3C2×C3×#13511yescharacteristic
748C2×C3C3×#57711yescharacteristic
749D3—22no—
750D3—41no—
751D3—81no—
752C22—32no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22C2×C3×D3×D411yescharacteristic
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—61no—
771C4—61no—
772C4—62no—
773C4—121no—
774C4—121no—
775C4C3×D3×#4111yescharacteristic
776C4C3×#100911yescharacteristic
777C3—21no—
778C3#8165511yescharacteristic, direct product factor
779C3C3×#330111yescharacteristic, complemented
780C2—62no—
781C2—81no—
782C2—121no—
783C2—241no—
784C2C3×#567611yescharacteristic
785C2C3×D3×#13511yescharacteristic
786C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#488C2
socleC22×C32C22×D4
hypercenterC3×#488D3
hypocenterC3C3×#3301
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#488

Complements

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

NH ≅ G/Ntype
1. C3×#5695C2semidirect
2. C3×#5677C2semidirect
3. C32×#488C2semidirect
4. C3×#5063C2semidirect
5. C3×#5057C2semidirect
6. C3×#4815C2semidirect
7. C3×#4807C2semidirect
8. C3×#4806C2semidirect
9. C3×D3×#103C2semidirect
10. C3×#4781C2semidirect
11. C3×#4777C2semidirect
12. C3×#4775C2semidirect
13. C3×#4772C2semidirect
14. C3×C4×#204C2semidirect
15. C3×C8×D12C2semidirect
17. #81655C3direct (N × H)
63. #5695C2×C3semidirect
64. #5677C2×C3semidirect
66. C3×#488D3semidirect
67. C3×#488C2×C3semidirect
80. #5063C2×C3semidirect
81. #5057C2×C3semidirect
82. #4815C2×C3semidirect
83. #4807C2×C3semidirect
84. #4806C2×C3semidirect
85. D3×#103C2×C3semidirect
86. #4781C2×C3semidirect
87. #4777C2×C3semidirect
88. #4775C2×C3semidirect
89. #4772C2×C3semidirect
90. C4×#204C2×C3semidirect
91. C8×D12C2×C3semidirect
281. #488C3×D3semidirect
692. C32#3301semidirect
778. C3#81655direct (N × H)
779. C3C3×#3301semidirect

Maximal subgroups

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

subgroupindex
C3×#56952
C3×#56772
C32×#4882
C3×#50632
C3×#50572
C3×#48152
C3×#48072
C3×#48062
C3×D3×#1032
C3×#47812
C3×#47772
C3×#47752
C3×#47722
C3×C4×#2042
C3×C8×D122
C3×#33013
#816553