Finite Group Databasebeta

← C3×#83512 #11888576

Subgroups — C3×#83512 #11888576

Order 1152.

934 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic, complemented
2C3×#5565C211yesmaximal, characteristic, complemented
3C3×#5238C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6C3×#5232C211yesmaximal, characteristic, complemented
7C3×#5083C211yesmaximal, characteristic, complemented
8C3×#5082C211yesmaximal, characteristic, complemented
9C3×#5049C211yesmaximal, characteristic, complemented
10C3×#5048C211yesmaximal, characteristic, complemented
11C3×#5045C211yesmaximal, characteristic, complemented
12C3×#5043C211yesmaximal, characteristic, complemented
13C3×#5014C211yesmaximal, characteristic, complemented
14C3×#5011C211yesmaximal, characteristic, complemented
15C3×#5009C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#83512C311yesmaximal, 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×#215C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#939—21no—
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#930C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#898—21no—
40C3×#883—21no—
41C3×#67⋊C4—21no—
42C3×C4×D12C2211yescharacteristic
43C3×#870C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#830C2211yescharacteristic
54C3×#830C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#553—31no—
62C3×#547—21no—
63C3×#547D311yescharacteristic, complemented
64C3×#547C2×C311yescharacteristic, complemented
65#5565C2×C311yescharacteristic, complemented
66C3×#491—31no—
67C3×#485—31no—
68C3×#483—31no—
69C3×#478—31no—
70C3×#468—31no—
71C3×#465—31no—
72C3×#461—31no—
73C3×#449—31no—
74C3×#449—31no—
75C3×#442—31no—
76C3×#435—31no—
77C3×#417—31no—
78C3×#416—31no—
79#5238C2×C311yescharacteristic, complemented
80#5238C2×C311yescharacteristic, complemented
81#5233C2×C311yescharacteristic, complemented
82#5232C2×C311yescharacteristic, complemented
83#5083C2×C311yescharacteristic, complemented
84#5082C2×C311yescharacteristic, complemented
85#5049C2×C311yescharacteristic, complemented
86#5048C2×C311yescharacteristic, complemented
87#5045C2×C311yescharacteristic, complemented
88#5043C2×C311yescharacteristic, complemented
89#5014C2×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
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4D411yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C22⋊C4D411yescharacteristic
122C32×C22⋊C4D411yescharacteristic
123C32×C42C2311yescharacteristic
124C3×#217—21no—
125C3×#215—41no—
126C3×#215—41no—
127C3×#213—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—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#3307—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×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×D8—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×#123—22no—
162C3×#123—22no—
163C3×#123—21no—
164C3×#123—21no—
165C3×#123—21no—
166C3×#123—21no—
167C3×#123—61no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C2×D311yescharacteristic
172C3×C22⋊Q8C22×C311yescharacteristic
173C3×C22⋊Q8C22×C311yescharacteristic
174C3×#121—22no—
175C3×#121—21no—
176C3×#121—21no—
177C3×#121—31no—
178C3×#121—31no—
179C3×#121—61no—
180C3×C4×D4—21no—
181C3×C4×D4—21no—
182C3×C4×D4—31no—
183C3×C4×D4—61no—
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C2×D311yescharacteristic
186C3×C4×D4C22×C311yescharacteristic
187C3×C4×D4C22×C311yescharacteristic
188C3×#117—31no—
189C2×C3×C4⋊C4—22no—
190C2×C3×C4⋊C4—21no—
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—31no—
193C2×#215C22×C311yescharacteristic
194C2×#215C22×C311yescharacteristic
195#939—21no—
196C2×#213C22×C311yescharacteristic
197#930C22×C311yescharacteristic
198#930C22×C311yescharacteristic
199#926C22×C311yescharacteristic
200C2×C4⋊Dic3C22×C311yescharacteristic
201C2×#208C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203#898—21no—
204#883—21no—
205#67⋊C4—21no—
206C4×D12C22×C311yescharacteristic
207#870C22×C311yescharacteristic
208C3×#107—31no—
209C3×#106—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×#102—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#809C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238#808C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—21no—
250C32×D4—21no—
251C32×D4—41no—
252C32×D4—42no—
253C32×D4—42no—
254C32×D4#4112yes—
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—21no—
262C2×C32×C4—42no—
263C2×C32×C4—42no—
264C2×C32×C4—42no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C3×#67—42no—
271C3×#67—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—81no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—81no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#553—31no—
284#547C3×D311yescharacteristic, complemented
285#491—31no—
286#485—31no—
287#483—31no—
288#478—31no—
289#468—31no—
290#465—31no—
291#461—31no—
292#449—31no—
293#449—31no—
294#442—31no—
295#435—31no—
296#417—31no—
297#416—31no—
298C3×#41—22no—
299C3×#41—22no—
300C3×#41—22no—
301C3×#41—22no—
302C3×#41—42no—
303C3×#41—42no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—41no—
308C3×#41—42no—
309C3×#41—42no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C23×C311yescharacteristic
315C2×C3×Q8C23×C311yescharacteristic
316C2×C3×D4—22no—
317C2×C3×D4—22no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4#6711yescharacteristic
328C2×C3×D4C3×D411yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C23×C311yescharacteristic
331C22×C3×C4—22no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C22×Dic3—21no—
351C2×D12C23×C311yescharacteristic
352C2×C4×D3—21no—
353C3×SD16—121no—
354C3×SD16—121no—
355C3×D8—62no—
356C3×M16—121no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—121no—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—31no—
379C3×C4⋊C4—61no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4#6711yescharacteristic
383C3×C4⋊C4C3×D411yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C4⋊C4C23×C311yescharacteristic
386C3×C22⋊C4—22no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4#6711yescharacteristic
402C3×C22⋊C4#6711yescharacteristic
403C3×C22⋊C4C3×D411yescharacteristic
404C3×C22⋊C4C3×D411yescharacteristic
405C3×C42—21no—
406C3×C42—61no—
407C3×C42C22×D311yescharacteristic
408C3×C42C23×C311yescharacteristic
409#217—21no—
410#215—41no—
411#215—41no—
412#213—22no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3C23×C311yescharacteristic
418C4⋊Dic3C23×C311yescharacteristic
419C4⋊Dic3C23×C311yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422C4×Dic3—21no—
423#208—41no—
424C2×C3⋊C8—41no—
425C2×C3⋊C8C23×C311yescharacteristic
426C2×C3⋊C8C23×C311yescharacteristic
427C2×C3⋊C8C23×C311yescharacteristic
428C2×C3⋊C8C23×C311yescharacteristic
429C22×C32—22no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32C22×D411yescharacteristic
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—41no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C2×#41C2×C3×D311yescharacteristic
455C2×#41C2×C3×D311yescharacteristic
456C2×SD16—31no—
457C2×SD16—31no—
458C2×D8—31no—
459C2×M16—31no—
460C22×C8—31no—
461C4⋊Q8C2×C3×D311yescharacteristic
462#126—61no—
463#125—31no—
464#123—21no—
465#123—21no—
466#123—61no—
467C22⋊Q8C2×C3×D311yescharacteristic
468C22⋊Q8C2×C3×D311yescharacteristic
469#121—21no—
470#121—31no—
471#121—31no—
472#121—61no—
473C4×D4—31no—
474C4×D4—61no—
475C4×D4C2×C3×D311yescharacteristic
476C4×D4C2×C3×D311yescharacteristic
477#117—31no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—31no—
480#107—31no—
481#106—31no—
482#106—31no—
483C4⋊C8—31no—
484#103—31no—
485#103—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494C22⋊C8—31no—
495C22⋊C8—31no—
496#97—31no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—61no—
503C23×C3C2×#6711yescharacteristic
504C23×C3C2×#6711yescharacteristic
505C23×C3C2×C3×D411yescharacteristic
506C23×C3C2×C3×D411yescharacteristic
507C22×D3—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—21no—
516C3×Q8—41no—
517C3×Q8—41no—
518C3×Q8—41no—
519C3×Q8—41no—
520C3×D4—22no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—22no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—42no—
527C3×D4—42no—
528C3×D4—42no—
529C3×D4—42no—
530C3×D4—42no—
531C3×D4—44no—
532C3×D4—44no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C3×D4—241no—
537C3×D4#23712yes—
538C3×D4C3×#4112yes—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
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—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—41no—
562C2×C3×C4—41no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—42no—
568C2×C3×C4—42no—
569C2×C3×C4—44no—
570C2×C3×C4—42no—
571C2×C3×C4—42no—
572C2×C3×C4—44no—
573C2×C3×C4—44no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—241no—
578C2×C3×C4—241no—
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C2×#6711yescharacteristic
581C2×C3×C4C2×#6711yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C2×C3×D411yescharacteristic
584C2×C3×C4C2×C3×D411yescharacteristic
585C2×C3×C4C2×C3×D411yescharacteristic
586C2×C3×C4C2×C3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C24×C311yescharacteristic
589#67—42no—
590#67—81no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—81no—
595D12—21no—
596D12—21no—
597C4×D3—81no—
598C3×C8—61no—
599C3×C8—61no—
600C3×C8—61no—
601C3×C8—61no—
602C3⋊C8—21no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C2×C32—42no—
607C2×C32—41no—
608C2×C32—41no—
609C2×C32#54611yescharacteristic
610C2×C32#57511yescharacteristic
611C2×C32#57711yescharacteristic
612C3×D3—81no—
613#41—22no—
614#41—22no—
615#41—41no—
616#41—41no—
617C2×Q8C22×C3×D311yescharacteristic
618C2×Q8C22×C3×D311yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—31no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4C3×#6711yescharacteristic
625C2×D4C22×C3×D311yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4C22×C3×D311yescharacteristic
632C22×C4C22×C3×D311yescharacteristic
633SD16—121no—
634SD16—121no—
635D8—62no—
636M16—121no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—121no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4C3×#6711yescharacteristic
653C4⋊C4C22×C3×D311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4C3×#6711yescharacteristic
662C22⋊C4C3×#6711yescharacteristic
663C42—61no—
664C42C22×C3×D311yescharacteristic
665C22×C3—24no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—21no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3C22×#6711yescharacteristic
697C22×C3C22×C3×D411yescharacteristic
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—22no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—42no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C2×#23711yescharacteristic
728C3×C4#100411yescharacteristic
729C3×C4C2×C3×#4111yescharacteristic
730C3×C4C3×H(5,𝔽2)11yescharacteristic
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734C32#330711yescharacteristic, complemented, Sylow
735C23—21no—
736C23—61no—
737C23C2×C3×#6711yescharacteristic
738C23C2×C3×#6711yescharacteristic
739Q8—21no—
740Q8—21no—
741Q8—21no—
742Q8—21no—
743D4—21no—
744D4—41no—
745D4—42no—
746D4—42no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—241no—
751D4C3×#23712yes—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—241no—
766C2×C4—241no—
767C2×C4C2×C3×#6711yescharacteristic
768C2×C4C2×C3×#6711yescharacteristic
769C2×C4C2×C3×#6711yescharacteristic
770C2×C4C2×C3×#6711yescharacteristic
771C2×C4C23×C3×D311yescharacteristic
772C8—61no—
773C8—61no—
774C8—61no—
775C8—61no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—44no—
780C2×C3—41no—
781C2×C3—41no—
782C2×C3—42no—
783C2×C3—41no—
784C2×C3—41no—
785C2×C3—42no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—241no—
789C2×C3#580611yescharacteristic
790C2×C3#582211yescharacteristic
791C2×C3#583711yescharacteristic
792C2×C3C3×#54611yescharacteristic
793C2×C3C3×#57511yescharacteristic
794C2×C3C3×#57711yescharacteristic
795D3—81no—
796C22—21no—
797C22—21no—
798C22—22no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22C22×C3×#6711yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—121no—
817C4—121no—
818C4—121no—
819C4C2×C3×#23711yescharacteristic
820C4C3×#100411yescharacteristic
821C3—21no—
822C3#8351211yescharacteristic, direct product factor
823C3C3×#330711yescharacteristic, complemented
824C2—41no—
825C2—41no—
826C2—42no—
827C2—241no—
828C2C3×#580611yescharacteristic
829C2C3×#582211yescharacteristic
830C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#547C2
socleC22×C32C22×D4
hypercenterC3×#547D3
hypocenterC3C3×#3307
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
1. C32×#547C2semidirect
2. C3×#5565C2semidirect
3. C3×#5238C2semidirect
4. C3×#5238C2semidirect
5. C3×#5233C2semidirect
6. C3×#5232C2semidirect
7. C3×#5083C2semidirect
8. C3×#5082C2semidirect
9. C3×#5049C2semidirect
10. C3×#5048C2semidirect
11. C3×#5045C2semidirect
12. C3×#5043C2semidirect
13. C3×#5014C2semidirect
14. C3×#5011C2semidirect
15. C3×#5009C2semidirect
17. #83512C3direct (N × H)
63. C3×#547D3semidirect
64. C3×#547C2×C3semidirect
65. #5565C2×C3semidirect
79. #5238C2×C3semidirect
80. #5238C2×C3semidirect
81. #5233C2×C3semidirect
82. #5232C2×C3semidirect
83. #5083C2×C3semidirect
84. #5082C2×C3semidirect
85. #5049C2×C3semidirect
86. #5048C2×C3semidirect
87. #5045C2×C3semidirect
88. #5043C2×C3semidirect
89. #5014C2×C3semidirect
90. #5011C2×C3semidirect
91. #5009C2×C3semidirect
284. #547C3×D3semidirect
734. C32#3307semidirect
822. C3#83512direct (N × H)
823. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
C3×#55652
C3×#52382
C3×#52332
C3×#52322
C3×#50832
C3×#50822
C3×#50492
C3×#50482
C3×#50452
C3×#50432
C3×#50142
C3×#50112
C3×#50092
C3×#33073
#835123