Finite Group Databasebeta

← C3×#83513 #11889808

Subgroups — C3×#83513 #11889808

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5232C211yesmaximal, characteristic, complemented
7C3×#5090C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5052C211yesmaximal, characteristic, complemented
10C3×#5051C211yesmaximal, characteristic, complemented
11C3×#5045C211yesmaximal, characteristic, complemented
12C3×#5044C211yesmaximal, characteristic, complemented
13C3×#5018C211yesmaximal, characteristic, complemented
14C3×#5011C211yesmaximal, characteristic, complemented
15C3×#5009C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#83513C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C32×#41C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic
21C32×#123—21no—
22C32×#123—21no—
23C32×C22⋊Q8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×#121—21no—
26C32×C4×D4C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C2×C32×C4⋊C4—21no—
29C2×C3×#216C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C3×#935—21no—
32C2×C3×#214C2211yescharacteristic
33C3×#926C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#889—21no—
40C3×#879—21no—
41C3×#877—21no—
42C3×#870C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#830C2211yescharacteristic
54C3×#830C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×#547—21no—
63C3×#547D311yescharacteristic
64C3×#547C2×C311yescharacteristic
65#5541C2×C311yescharacteristic, complemented
66C3×#491—31no—
67C3×#485—31no—
68C3×#484—31no—
69C3×#478—31no—
70C3×#470—31no—
71C3×#467—31no—
72C3×#462—31no—
73C3×#452—31no—
74C3×#452—31no—
75C3×#440—31no—
76C3×#435—31no—
77C3×#417—31no—
78C3×#416—31no—
79#5239C2×C311yescharacteristic, complemented
80#5239C2×C311yescharacteristic, complemented
81#5233C2×C311yescharacteristic, complemented
82#5232C2×C311yescharacteristic, complemented
83#5090C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5052C2×C311yescharacteristic, complemented
86#5051C2×C311yescharacteristic, complemented
87#5045C2×C311yescharacteristic, complemented
88#5044C2×C311yescharacteristic, complemented
89#5018C2×C311yescharacteristic, complemented
90#5011C2×C311yescharacteristic, complemented
91#5009C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—22no—
94C32×#41—41no—
95C32×#41—41no—
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4D411yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4—21no—
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3×Dic3—21no—
108C2×C3×Dic6C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4D411yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C22⋊C4D411yescharacteristic
119C32×C22⋊C4D411yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#216—41no—
125C3×#216—41no—
126C3×#214—22no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×#208—41no—
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3315—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41—21no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C2×D311yescharacteristic
149C2×C3×#41C22×C311yescharacteristic
150C2×C3×#41C22×C311yescharacteristic
151C2×C3×Q16—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C2×C3×M16—31no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—21no—
157C3×C4⋊Q8C2×D311yescharacteristic
158C3×C4⋊Q8C22×C311yescharacteristic
159C3×#126—61no—
160C3×#125—31no—
161C3×#125—61no—
162C3×#123—22no—
163C3×#123—22no—
164C3×#123—21no—
165C3×#123—21no—
166C3×#123—21no—
167C3×#123—21no—
168C3×#123—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×C22⋊Q8C22×C311yescharacteristic
176C3×C22⋊Q8C22×C311yescharacteristic
177C3×#121—22no—
178C3×#121—21no—
179C3×#121—21no—
180C3×C4×Q8—31no—
181C3×C4×D4—21no—
182C3×C4×D4—21no—
183C3×C4×D4C2×D311yescharacteristic
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C22×C311yescharacteristic
186C3×C4×D4C22×C311yescharacteristic
187C3×#117—31no—
188C3×#117—61no—
189C2×C3×C4⋊C4—22no—
190C2×C3×C4⋊C4—21no—
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—31no—
193C2×#216C22×C311yescharacteristic
194C2×#216C22×C311yescharacteristic
195#935—21no—
196C2×#214C22×C311yescharacteristic
197#926C22×C311yescharacteristic
198C2×C4⋊Dic3C22×C311yescharacteristic
199#924C22×C311yescharacteristic
200#924C22×C311yescharacteristic
201C2×#208C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203#889—21no—
204#879—21no—
205#877—21no—
206#870C22×C311yescharacteristic
207C4×Dic6C22×C311yescharacteristic
208C3×#107—31no—
209C3×#107—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#832C22×C311yescharacteristic
234#830C22×C311yescharacteristic
235#830C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238#807C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×D4—21no—
250C32×D4—41no—
251C32×D4—42no—
252C32×D4—42no—
253C32×D4#4112yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—42no—
262C2×C32×C4—42no—
263C2×C32×C4—42no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—42no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280#552—31no—
281#547C3×D311yescharacteristic
282#491—31no—
283#485—31no—
284#484—31no—
285#478—31no—
286#470—31no—
287#467—31no—
288#462—31no—
289#452—31no—
290#452—31no—
291#440—31no—
292#435—31no—
293#417—31no—
294#416—31no—
295C3×#41—22no—
296C3×#41—22no—
297C3×#41—22no—
298C3×#41—22no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41—41no—
302C3×#41—41no—
303C3×#41—41no—
304C3×#41—41no—
305C3×#41—42no—
306C3×#41—42no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—31no—
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C23×C311yescharacteristic
313C2×C3×Q8C23×C311yescharacteristic
314C2×C3×D4—22no—
315C2×C3×D4—22no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4#6711yescharacteristic
323C2×C3×D4C3×D411yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C23×C311yescharacteristic
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C23×C311yescharacteristic
341C22×C3×C4C23×C311yescharacteristic
342C22×Dic3—21no—
343C2×Dic6C23×C311yescharacteristic
344C3×Q16—121no—
345C3×Q16—121no—
346C3×SD16—62no—
347C3×M16—121no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—22no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4#6711yescharacteristic
377C3×C4⋊C4C3×D411yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C23×C311yescharacteristic
380C3×C22⋊C4—22no—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4#6711yescharacteristic
395C3×C22⋊C4#6711yescharacteristic
396C3×C22⋊C4C3×D411yescharacteristic
397C3×C22⋊C4C3×D411yescharacteristic
398C3×C42—21no—
399C3×C42—61no—
400C3×C42—61no—
401C3×C42C22×D311yescharacteristic
402C3×C42C23×C311yescharacteristic
403#217—21no—
404#217—21no—
405#217—21no—
406#216—41no—
407#216—41no—
408#214—22no—
409C4⋊Dic3—21no—
410C4⋊Dic3C23×C311yescharacteristic
411C4⋊Dic3C23×C311yescharacteristic
412C4⋊Dic3C23×C311yescharacteristic
413Dic3⋊C4—21no—
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418C4×Dic3—21no—
419C4×Dic3—21no—
420#208—41no—
421C2×C3⋊C8—41no—
422C2×C3⋊C8C23×C311yescharacteristic
423C2×C3⋊C8C23×C311yescharacteristic
424C2×C3⋊C8C23×C311yescharacteristic
425C2×C3⋊C8C23×C311yescharacteristic
426C22×C32—22no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32C22×D411yescharacteristic
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4C2×#4111yescharacteristic
444C32×C4H(5,𝔽2)11yescharacteristic
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C2×#41C2×C3×D311yescharacteristic
450C2×#41C2×C3×D311yescharacteristic
451C2×Q16—31no—
452C2×Q16—31no—
453C2×SD16—31no—
454C2×M16—31no—
455C22×C8—31no—
456C4⋊Q8C2×C3×D311yescharacteristic
457#126—61no—
458#125—31no—
459#125—61no—
460#123—21no—
461#123—21no—
462#123—61no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8C2×C3×D311yescharacteristic
466C22⋊Q8C2×C3×D311yescharacteristic
467#121—21no—
468C4×Q8—31no—
469C4×D4C2×C3×D311yescharacteristic
470C4×D4C2×C3×D311yescharacteristic
471#117—31no—
472#117—61no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—31no—
475#107—31no—
476#107—31no—
477#106—31no—
478C4⋊C8—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—31no—
485#103—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489C22⋊C8—31no—
490C22⋊C8—31no—
491#97—31no—
492C23×C3—22no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3C2×#6711yescharacteristic
498C23×C3C2×#6711yescharacteristic
499C23×C3C2×C3×D411yescharacteristic
500C23×C3C2×C3×D411yescharacteristic
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×Q8—41no—
512C3×Q8—41no—
513C3×Q8—61no—
514C3×Q8—61no—
515C3×D4—22no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—42no—
522C3×D4—42no—
523C3×D4—42no—
524C3×D4—42no—
525C3×D4—42no—
526C3×D4—44no—
527C3×D4—44no—
528C3×D4#23712yes—
529C3×D4C3×#4112yes—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—42no—
557C2×C3×C4—42no—
558C2×C3×C4—42no—
559C2×C3×C4—42no—
560C2×C3×C4—44no—
561C2×C3×C4—42no—
562C2×C3×C4—42no—
563C2×C3×C4—44no—
564C2×C3×C4—44no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—122no—
570C2×C3×C4C2×#6711yescharacteristic
571C2×C3×C4C2×#6711yescharacteristic
572C2×C3×C4C2×#6711yescharacteristic
573C2×C3×C4C2×#6711yescharacteristic
574C2×C3×C4C2×C3×D411yescharacteristic
575C2×C3×C4C2×C3×D411yescharacteristic
576C2×C3×C4C2×C3×D411yescharacteristic
577C2×C3×C4C2×C3×D411yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C24×C311yescharacteristic
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—42no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—61no—
588C3×C8—61no—
589C3×C8—61no—
590C3×C8—61no—
591C3⋊C8—21no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32—42no—
596C2×C32—41no—
597C2×C32—41no—
598C2×C32#54611yescharacteristic
599C2×C32#57511yescharacteristic
600C2×C32#57811yescharacteristic
601#41—22no—
602#41—22no—
603#41—41no—
604#41—41no—
605C2×Q8—31no—
606C2×Q8C22×C3×D311yescharacteristic
607C2×Q8C22×C3×D311yescharacteristic
608C2×D4—21no—
609C2×D4—21no—
610C2×D4C3×#6711yescharacteristic
611C2×D4C22×C3×D311yescharacteristic
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—61no—
616C22×C4C22×C3×D311yescharacteristic
617C22×C4C22×C3×D311yescharacteristic
618Q16—121no—
619Q16—121no—
620SD16—62no—
621M16—121no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—121no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—31no—
632C4⋊C4—31no—
633C4⋊C4—31no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4C3×#6711yescharacteristic
641C4⋊C4C22×C3×D311yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4C3×#6711yescharacteristic
649C22⋊C4C3×#6711yescharacteristic
650C42—61no—
651C42—61no—
652C42C22×C3×D311yescharacteristic
653C22×C3—24no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—22no—
668C22×C3—21no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3C22×#6711yescharacteristic
682C22×C3C22×C3×D411yescharacteristic
683C3×C4—22no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—42no—
698C3×C4—42no—
699C3×C4—42no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4C2×#23711yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4C2×C3×#4111yescharacteristic
713C3×C4C3×H(5,𝔽2)11yescharacteristic
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718C32#331511yescharacteristic, complemented, Sylow
719C23—21no—
720C23C2×C3×#6711yescharacteristic
721C23C2×C3×#6711yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—61no—
727Q8—61no—
728D4—21no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4C3×#23712yes—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—122no—
748C2×C4C2×C3×#6711yescharacteristic
749C2×C4C2×C3×#6711yescharacteristic
750C2×C4C2×C3×#6711yescharacteristic
751C2×C4C2×C3×#6711yescharacteristic
752C2×C4C23×C3×D311yescharacteristic
753C8—61no—
754C8—61no—
755C8—61no—
756C8—61no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—44no—
761C2×C3—41no—
762C2×C3—41no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—42no—
767C2×C3—81no—
768C2×C3—81no—
769C2×C3#580611yescharacteristic
770C2×C3#582211yescharacteristic
771C2×C3#583811yescharacteristic
772C2×C3C3×#54611yescharacteristic
773C2×C3C3×#57511yescharacteristic
774C2×C3C3×#57811yescharacteristic
775C22—21no—
776C22—21no—
777C22—22no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—41no—
783C22—41no—
784C22C22×C3×#6711yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4C2×C3×#23711yescharacteristic
797C4C3×#100411yescharacteristic
798C3—21no—
799C3#8351311yescharacteristic, direct product factor
800C3C3×#331511yescharacteristic, complemented
801C2—41no—
802C2—41no—
803C2—42no—
804C2C3×#580611yescharacteristic
805C2C3×#582211yescharacteristic
806C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#547C2
socleC22×C32C22×D4
hypercenterC3×#547D3
hypocenterC3C3×#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C3×#5239C2semidirect
4. C3×#5239C2semidirect
5. C3×#5233C2semidirect
6. C3×#5232C2semidirect
7. C3×#5090C2semidirect
8. C3×#5082C2semidirect
9. C3×#5052C2semidirect
10. C3×#5051C2semidirect
11. C3×#5045C2semidirect
12. C3×#5044C2semidirect
13. C3×#5018C2semidirect
14. C3×#5011C2semidirect
15. C3×#5009C2semidirect
17. #83513C3direct (N × H)
65. #5541C2×C3semidirect
79. #5239C2×C3semidirect
80. #5239C2×C3semidirect
81. #5233C2×C3semidirect
82. #5232C2×C3semidirect
83. #5090C2×C3semidirect
84. #5082C2×C3semidirect
85. #5052C2×C3semidirect
86. #5051C2×C3semidirect
87. #5045C2×C3semidirect
88. #5044C2×C3semidirect
89. #5018C2×C3semidirect
90. #5011C2×C3semidirect
91. #5009C2×C3semidirect
718. C32#3315semidirect
799. C3#83513direct (N × H)
800. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
C3×#55412
C3×#52392
C3×#52332
C3×#52322
C3×#50902
C3×#50822
C3×#50522
C3×#50512
C3×#50452
C3×#50442
C3×#50182
C3×#50112
C3×#50092
C3×#33153
#835133