Finite Group Databasebeta

← C3×#85908 #11909731

Subgroups — C3×#85908 #11909731

Order 1152.

2355 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#520C211yesmaximal, characteristic, complemented
2C3×#5834C211yesmaximal, characteristic, complemented
3C3×#5831C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×#5574C211yesmaximal, characteristic, complemented
6C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
7C3×Q8×Dic6C211yesmaximal, characteristic, complemented
8C3×#5561C213yesmaximal, complemented
9C3×#5559C213yesmaximal, complemented
10C3×#5551C213yesmaximal, complemented
11C3×#5548C213yesmaximal, complemented
12C3×#5534C213yesmaximal, complemented
13C3×#5528C213yesmaximal, complemented
14C3×#5511C213yesmaximal, complemented
15C3×#5507C213yesmaximal, complemented
16C3×#3522—31nomaximal
17#85908C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×#235C2216yes—
22C32×C4×Q8C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C32×C4×D4C2213yes—
25C32×C4×D4C2213yes—
26C32×#117C2213yes—
27C2×C32×C4⋊C4C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#940C2213yes—
31C3×#938C2213yes—
32C3×#938C2213yes—
33C3×#936C2213yes—
34C3×#930C2213yes—
35C3×#929C2216yes—
36C3×C4×#67C2213yes—
37C3×C4×#67C2213yes—
38C3×C4×#67C2216yes—
39C3×#924C2213yes—
40C3×#924C2216yes—
41C3×#898C2213yes—
42C3×#897C2213yes—
43C3×#896C2216yes—
44C3×#896C2211yescharacteristic
45C3×#895C2213yes—
46C3×#894C2213yes—
47C3×#893C2213yes—
48C3×D3×C4⋊C4C2213yes—
49C3×D3×C4⋊C4C2213yes—
50C3×#889C2213yes—
51C3×#888C2213yes—
52C3×#888C2213yes—
53C3×#887C2213yes—
54C3×#885C2213yes—
55C3×#885C2216yes—
56C3×#884C2213yes—
57C3×#883C2213yes—
58C3×#883C2216yes—
59C3×#879C2213yes—
60C3×#875C2213yes—
61C3×C4×D12C2213yes—
62C3×C4×D12C2213yes—
63C3×#872C2213yes—
64C3×C42×D3C2213yes—
65C3×#869C2213yes—
66C3×C4×Dic6C2213yes—
67C3×C4×Dic6C2213yes—
68C3×#559—33no—
69C3×Q82—31no—
70C3×#554—33no—
71C3×#550—31no—
72C3×#548—31no—
73C3×#548—31no—
74C3×#547—33no—
75C3×#547—33no—
76C3×#542—33no—
77C3×#542—33no—
78C3×#532—33no—
79C3×#529—33no—
80C3×#520—21no—
81C3×#520—31no—
82C3×#520D311yescharacteristic, complemented
83C3×#520C2×C311yescharacteristic, complemented
84C2×C3×C4×Q8—31no—
85#5834C2×C311yescharacteristic, complemented
86#5831C2×C311yescharacteristic, complemented
87#5576C2×C311yescharacteristic, complemented
88#5574C2×C311yescharacteristic, complemented
89C4×D3×Q8C2×C311yescharacteristic, complemented
90Q8×Dic6C2×C311yescharacteristic, complemented
91#5561C2×C313yescomplemented
92#5559C2×C313yescomplemented
93#5551C2×C313yescomplemented
94#5548C2×C313yescomplemented
95#5534C2×C313yescomplemented
96#5528C2×C313yescomplemented
97#5511C2×C313yescomplemented
98#5507C2×C313yescomplemented
99C32×#41—24no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2313yes—
102C22×C32×C4C2313yes—
103C22×C32×C4C2316yes—
104C2×C3×#67C2313yes—
105C2×C3×#67C2313yes—
106C2×C3×#67C2316yes—
107C3×#239—24no—
108C3×D3×Q8—24no—
109C3×#235—412no—
110C2×C3×D12C2313yes—
111C2×C3×D12C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2316yes—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2313yes—
119C2×C3×Dic6C2316yes—
120C32×C4⋊C4C2313yes—
121C32×C4⋊C4C2313yes—
122C32×C4⋊C4C2313yes—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4C2313yes—
125C32×C22⋊C4C2313yes—
126C32×C42C2313yes—
127C32×C42C2313yes—
128C3×#217C2313yes—
129C3×#217C2313yes—
130C3×#217C2316yes—
131C3×(C2×D3)⋊C4C2311yescharacteristic
132C3×(C2×D3)⋊C4C2313yes—
133C3×(C2×D3)⋊C4C2313yes—
134C3×(C2×D3)⋊C4C2313yes—
135C3×(C2×D3)⋊C4C2316yes—
136C3×(C2×D3)⋊C4C2311yescharacteristic
137C3×(C2×D3)⋊C4C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×C4⋊Dic3C2313yes—
141C3×C4⋊Dic3C2313yes—
142C3×Dic3⋊C4C2311yescharacteristic
143C3×Dic3⋊C4C2313yes—
144C3×Dic3⋊C4C2316yes—
145C3×Dic3⋊C4C2313yes—
146C3×Dic3⋊C4C2313yes—
147C3×Dic3⋊C4C2311yescharacteristic
148C3×Dic3⋊C4C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152C3×C4×Dic3C2313yes—
153#3522—31noSylow
154C2×C3×#41—21no—
155C2×C3×#41—31no—
156C2×C3×#41—36no—
157C2×C3×#41C2×D311yescharacteristic
158C2×C3×#41C22×C311yescharacteristic
159C22×C3×Q8—31no—
160C2×#239C22×C311yescharacteristic
161C2×D3×Q8C22×C311yescharacteristic
162C2×#235C22×C316yes—
163C3×C4⋊Q8—33no—
164C3×C4⋊Q8—33no—
165C3×C4⋊Q8—33no—
166C3×#127—33no—
167C3×#126—33no—
168C3×#126—33no—
169C3×#125—33no—
170C3×#124—33no—
171C3×#124—33no—
172C3×#124—36no—
173C3×#124—33no—
174C3×#123—36no—
175C3×#123—33no—
176C3×#123—36no—
177C3×#123—33no—
178C3×C22⋊Q8—36no—
179C3×C22⋊Q8—33no—
180C3×C22⋊Q8—31no—
181C3×C22⋊Q8—36no—
182C3×C22⋊Q8—33no—
183C3×#121—33no—
184C3×#121—33no—
185C3×#121—33no—
186C3×#121—33no—
187C3×#121—33no—
188C3×C4×Q8—21no—
189C3×C4×Q8—21no—
190C3×C4×Q8—31no—
191C3×C4×Q8—31no—
192C3×C4×Q8—33no—
193C3×C4×Q8—33no—
194C3×C4×Q8—33no—
195C3×C4×Q8C2×D311yescharacteristic
196C3×C4×Q8C2×D311yescharacteristic
197C3×C4×Q8C22×C311yescharacteristic
198C3×C4×Q8C22×C311yescharacteristic
199C3×C4×D4—23no—
200C3×C4×D4—23no—
201C3×C4×D4—36no—
202C3×C4×D4—33no—
203C3×C4×D4—33no—
204C3×C4×D4—33no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×C4×D4C2×D313yes—
208C3×C4×D4C2×D313yes—
209C3×C4×D4C22×C313yes—
210C3×C4×D4C22×C313yes—
211C3×#117—23no—
212C3×#117—33no—
213C3×#117C2×D313yes—
214C3×#117C22×C313yes—
215C2×C3×C4⋊C4—23no—
216C2×C3×C4⋊C4—33no—
217C2×C3×C4⋊C4—33no—
218C2×C3×C4⋊C4C2×D313yes—
219C2×C3×C4⋊C4C22×C313yes—
220C2×C3×C42—33no—
221Q8×Dic3C22×C311yescharacteristic
222Q8×Dic3C22×C311yescharacteristic
223#940C22×C313yes—
224#938C22×C313yes—
225#938C22×C313yes—
226#936C22×C313yes—
227#930C22×C313yes—
228#929C22×C316yes—
229C4×#67C22×C313yes—
230C4×#67C22×C313yes—
231C4×#67C22×C316yes—
232#924C22×C313yes—
233#924C22×C316yes—
234#898C22×C313yes—
235#897C22×C313yes—
236#896C22×C316yes—
237#896C22×C311yescharacteristic
238#895C22×C313yes—
239#894C22×C313yes—
240#893C22×C313yes—
241D3×C4⋊C4C22×C313yes—
242D3×C4⋊C4C22×C313yes—
243#889C22×C313yes—
244#888C22×C313yes—
245#888C22×C313yes—
246#887C22×C313yes—
247#885C22×C313yes—
248#885C22×C316yes—
249#884C22×C313yes—
250#883C22×C313yes—
251#883C22×C316yes—
252#879C22×C313yes—
253#875C22×C313yes—
254C4×D12C22×C313yes—
255C4×D12C22×C313yes—
256#872C22×C313yes—
257C42×D3C22×C313yes—
258#869C22×C313yes—
259C4×Dic6C22×C313yes—
260C4×Dic6C22×C313yes—
261C23×C32C2413yes—
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C32×D4—26no—
266C2×C32×C4—26no—
267C2×C32×C4—46no—
268C2×C32×C4C2411yescharacteristic
269C2×C32×C4C2413yes—
270C2×C32×C4C2411yescharacteristic
271C2×C32×C4C2413yes—
272C2×C32×C4C2411yescharacteristic
273C2×C32×C4C2413yes—
274C3×#67—26no—
275C3×#67—26no—
276C3×#67—46no—
277C2×C3×Dic3C2411yescharacteristic
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2411yescharacteristic
282C2×C3×Dic3C2411yescharacteristic
283C3×D12—26no—
284C3×D12—26no—
285C3×C4×D3—26no—
286C3×C4×D3—26no—
287C3×C4×D3—26no—
288C3×C4×D3—22no—
289C3×C4×D3—46no—
290C3×Dic6—26no—
291C3×Dic6—22no—
292C3×Dic6—46no—
293#559—33no—
294Q82—31no—
295#554—33no—
296#550—31no—
297#548—31no—
298#548—31no—
299#547—33no—
300#547—33no—
301#542—33no—
302#542—33no—
303#532—33no—
304#529—33no—
305#520—31no—
306#520C3×D311yescharacteristic, complemented
307C2×C4×Q8—31no—
308C3×#41—28no—
309C3×#41—24no—
310C3×#41—24no—
311C3×#41—64no—
312C3×#41—1212no—
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—33no—
316C2×C3×Q8—36no—
317C2×C3×Q8—64no—
318C2×C3×Q8C22×D311yescharacteristic
319C2×C3×Q8C23×C311yescharacteristic
320C2×C3×D4—23no—
321C2×C3×D4—33no—
322C2×C3×D4—33no—
323C2×C3×D4—36no—
324C2×C3×D4—33no—
325C2×C3×D4—33no—
326C2×C3×D4C22×D313yes—
327C2×C3×D4C23×C313yes—
328C22×C3×C4—23no—
329C22×C3×C4—26no—
330C22×C3×C4—31no—
331C22×C3×C4—33no—
332C22×C3×C4—33no—
333C22×C3×C4—33no—
334C22×C3×C4—36no—
335C22×C3×C4C22×D313yes—
336C22×C3×C4C22×D316yes—
337C22×C3×C4C23×C313yes—
338C22×C3×C4C23×C316yes—
339C2×#67C23×C313yes—
340C2×#67C23×C313yes—
341C2×#67C23×C316yes—
342#239—24no—
343D3×Q8—24no—
344#235—412no—
345C2×D12C23×C313yes—
346C2×D12C23×C313yes—
347C2×C4×D3C23×C311yescharacteristic
348C2×C4×D3C23×C313yes—
349C2×C4×D3C23×C313yes—
350C2×C4×D3C23×C313yes—
351C2×C4×D3C23×C316yes—
352C2×Dic6C23×C311yescharacteristic
353C2×Dic6C23×C313yes—
354C2×Dic6C23×C316yes—
355C3×C4⋊C4—23no—
356C3×C4⋊C4—23no—
357C3×C4⋊C4—23no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—36no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—33no—
367C3×C4⋊C4—33no—
368C3×C4⋊C4—33no—
369C3×C4⋊C4—33no—
370C3×C4⋊C4C22×D313yes—
371C3×C4⋊C4C22×D313yes—
372C3×C4⋊C4C22×D313yes—
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C23×C313yes—
375C3×C4⋊C4C23×C313yes—
376C3×C4⋊C4C23×C313yes—
377C3×C4⋊C4C23×C311yescharacteristic
378C3×C22⋊C4—23no—
379C3×C22⋊C4—23no—
380C3×C22⋊C4—33no—
381C3×C22⋊C4—36no—
382C3×C22⋊C4—33no—
383C3×C22⋊C4—33no—
384C3×C22⋊C4—33no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—31no—
387C3×C22⋊C4—33no—
388C3×C22⋊C4—36no—
389C3×C22⋊C4—33no—
390C3×C22⋊C4C22×D313yes—
391C3×C22⋊C4C22×D313yes—
392C3×C22⋊C4C23×C313yes—
393C3×C22⋊C4C23×C313yes—
394C3×C42—23no—
395C3×C42—23no—
396C3×C42—33no—
397C3×C42—33no—
398C3×C42—33no—
399C3×C42—33no—
400C3×C42C22×D313yes—
401C3×C42C22×D313yes—
402C3×C42C23×C313yes—
403C3×C42C23×C313yes—
404#217C23×C313yes—
405#217C23×C313yes—
406#217C23×C316yes—
407(C2×D3)⋊C4C23×C313yes—
408(C2×D3)⋊C4C23×C313yes—
409(C2×D3)⋊C4C23×C311yescharacteristic
410(C2×D3)⋊C4C23×C313yes—
411(C2×D3)⋊C4C23×C316yes—
412(C2×D3)⋊C4C23×C311yescharacteristic
413(C2×D3)⋊C4C23×C313yes—
414C4⋊Dic3C23×C313yes—
415C4⋊Dic3C23×C313yes—
416C4⋊Dic3C23×C313yes—
417C4⋊Dic3C23×C313yes—
418Dic3⋊C4C23×C313yes—
419Dic3⋊C4C23×C316yes—
420Dic3⋊C4C23×C313yes—
421Dic3⋊C4C23×C311yescharacteristic
422Dic3⋊C4C23×C313yes—
423Dic3⋊C4C23×C311yescharacteristic
424Dic3⋊C4C23×C313yes—
425C4×Dic3C23×C313yes—
426C4×Dic3C23×C313yes—
427C4×Dic3C23×C313yes—
428C4×Dic3C23×C313yes—
429C22×C32—23no—
430C22×C32—23no—
431C22×C32—23no—
432C22×C32C2511yescharacteristic
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—23no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3H(5,𝔽2)12yes—
439C32×C4—21no—
440C32×C4—23no—
441C32×C4—23no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4C2×#4116yes—
445C3×Dic3—23no—
446C3×Dic3—21no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic32−1+412yes—
451C2×#41—31no—
452C2×#41—36no—
453C2×#41C2×C3×D311yescharacteristic
454C22×Q8—31no—
455C4⋊Q8—33no—
456C4⋊Q8—33no—
457C4⋊Q8—33no—
458#127—33no—
459#126—33no—
460#126—33no—
461#125—33no—
462#124—33no—
463#124—33no—
464#124—36no—
465#124—33no—
466#123—36no—
467#123—33no—
468#123—33no—
469#123—36no—
470C22⋊Q8—36no—
471C22⋊Q8—33no—
472C22⋊Q8—31no—
473C22⋊Q8—36no—
474C22⋊Q8—33no—
475#121—33no—
476#121—33no—
477#121—33no—
478#121—33no—
479#121—33no—
480C4×Q8—31no—
481C4×Q8—31no—
482C4×Q8—33no—
483C4×Q8—33no—
484C4×Q8—33no—
485C4×Q8C2×C3×D311yescharacteristic
486C4×Q8C2×C3×D311yescharacteristic
487C4×D4—33no—
488C4×D4—33no—
489C4×D4—36no—
490C4×D4—33no—
491C4×D4—33no—
492C4×D4—33no—
493C4×D4C2×C3×D313yes—
494C4×D4C2×C3×D313yes—
495#117—33no—
496#117C2×C3×D313yes—
497C2×C4⋊C4—33no—
498C2×C4⋊C4—33no—
499C2×C4⋊C4C2×C3×D313yes—
500C2×C42—33no—
501C23×C3—23no—
502C23×C3—31no—
503C23×C3—33no—
504C23×C3C23×D313yes—
505C23×C3C24×C313yes—
506C22×D3C24×C313yes—
507C22×D3C24×C311yescharacteristic
508C3×Q8—24no—
509C3×Q8—62no—
510C3×Q8—66no—
511C3×Q8—126no—
512C3×Q8#23514yescomplemented
513C3×Q8C3×#4114yescomplemented
514C3×D4—212no—
515C3×D4—26no—
516C3×D4—26no—
517C3×D4—66no—
518C3×D4—66no—
519C3×D4—66no—
520C3×D4—66no—
521C3×D4—126no—
522C2×C3×C4—212no—
523C2×C3×C4—26no—
524C2×C3×C4—26no—
525C2×C3×C4—23no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—23no—
530C2×C3×C4—23no—
531C2×C3×C4—31no—
532C2×C3×C4—31no—
533C2×C3×C4—33no—
534C2×C3×C4—33no—
535C2×C3×C4—33no—
536C2×C3×C4—31no—
537C2×C3×C4—46no—
538C2×C3×C4—46no—
539C2×C3×C4—62no—
540C2×C3×C4—66no—
541C2×C3×C4—66no—
542C2×C3×C4—66no—
543C2×C3×C4—86no—
544C2×C3×C4—126no—
545C2×C3×C4C23×D311yescharacteristic
546C2×C3×C4C23×D313yes—
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C23×D313yes—
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D313yes—
551C2×C3×C4C24×C311yescharacteristic
552C2×C3×C4C24×C313yes—
553C2×C3×C4C24×C311yescharacteristic
554C2×C3×C4C24×C313yes—
555C2×C3×C4C24×C311yescharacteristic
556C2×C3×C4C24×C313yes—
557#67—26no—
558#67—26no—
559#67—46no—
560C2×Dic3C24×C311yescharacteristic
561C2×Dic3C24×C313yes—
562C2×Dic3C24×C313yes—
563C2×Dic3C24×C313yes—
564C2×Dic3C24×C311yescharacteristic
565C2×Dic3C24×C311yescharacteristic
566D12—26no—
567D12—26no—
568C4×D3—26no—
569C4×D3—26no—
570C4×D3—26no—
571C4×D3—22no—
572C4×D3—46no—
573Dic6—26no—
574Dic6—22no—
575Dic6—46no—
576C2×C32—43no—
577C2×C32C22×#4111yescharacteristic
578C2×C32C2×H(5,𝔽2)11yescharacteristic
579C2×C32C2×2−1+411yescharacteristic
580C3×D3—22no—
581C3×D3—43no—
582#41—24no—
583#41—64no—
584#41—1212no—
585C2×Q8—31no—
586C2×Q8—33no—
587C2×Q8—36no—
588C2×Q8—64no—
589C2×Q8C22×C3×D311yescharacteristic
590C2×D4—33no—
591C2×D4—33no—
592C2×D4—36no—
593C2×D4—33no—
594C2×D4—33no—
595C2×D4C22×C3×D313yes—
596C22×C4—31no—
597C22×C4—33no—
598C22×C4—33no—
599C22×C4—33no—
600C22×C4—36no—
601C22×C4C22×C3×D313yes—
602C22×C4C22×C3×D316yes—
603C4⋊C4—33no—
604C4⋊C4—33no—
605C4⋊C4—33no—
606C4⋊C4—36no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—33no—
610C4⋊C4—33no—
611C4⋊C4—33no—
612C4⋊C4—33no—
613C4⋊C4—33no—
614C4⋊C4C22×C3×D313yes—
615C4⋊C4C22×C3×D313yes—
616C4⋊C4C22×C3×D313yes—
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—33no—
619C22⋊C4—36no—
620C22⋊C4—33no—
621C22⋊C4—33no—
622C22⋊C4—33no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—33no—
626C22⋊C4—36no—
627C22⋊C4—33no—
628C22⋊C4C22×C3×D313yes—
629C22⋊C4C22×C3×D313yes—
630C42—33no—
631C42—33no—
632C42—33no—
633C42—33no—
634C42C22×C3×D313yes—
635C42C22×C3×D313yes—
636C22×C3—26no—
637C22×C3—23no—
638C22×C3—23no—
639C22×C3—23no—
640C22×C3—23no—
641C22×C3—23no—
642C22×C3—23no—
643C22×C3—21no—
644C22×C3—32no—
645C22×C3—43no—
646C22×C3—43no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—63no—
650C22×C3—63no—
651C22×C3—63no—
652C22×C3C24×D311yescharacteristic
653C22×C3C25×C311yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—23no—
657C2×D3—23no—
658C2×D3—23no—
659C2×D3C3×H(5,𝔽2)12yes—
660C3×C4—22no—
661C3×C4—21no—
662C3×C4—23no—
663C3×C4—23no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—23no—
668C3×C4—23no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—26no—
672C3×C4—32no—
673C3×C4—43no—
674C3×C4—43no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—63no—
679C3×C4—63no—
680C3×C4—63no—
681C3×C4—61no—
682C3×C4C2×#23516yes—
683C3×C4C2×C3×#4116yes—
684Dic3—23no—
685Dic3—21no—
686Dic3—23no—
687Dic3—23no—
688Dic3—21no—
689Dic3C3×2−1+412yes—
690C32#352211yescharacteristic, complemented, Sylow
691C23—31no—
692C23—33no—
693C23C23×C3×D313yes—
694Q8—62no—
695Q8—66no—
696Q8—126no—
697Q8C3×#23514yescomplemented
698D4—26no—
699D4—66no—
700D4—66no—
701D4—66no—
702D4—66no—
703D4—126no—
704C2×C4—26no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—33no—
708C2×C4—33no—
709C2×C4—33no—
710C2×C4—31no—
711C2×C4—46no—
712C2×C4—62no—
713C2×C4—66no—
714C2×C4—66no—
715C2×C4—66no—
716C2×C4—126no—
717C2×C4C23×C3×D311yescharacteristic
718C2×C4C23×C3×D313yes—
719C2×C4C23×C3×D311yescharacteristic
720C2×C4C23×C3×D313yes—
721C2×C4C23×C3×D311yescharacteristic
722C2×C4C23×C3×D313yes—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—46no—
727C2×C3—43no—
728C2×C3—43no—
729C2×C3—62no—
730C2×C3—123no—
731C2×C3C22×#23511yescharacteristic
732C2×C3D3×H(5,𝔽2)11yescharacteristic
733C2×C3D3×2−1+411yescharacteristic
734C2×C3C22×C3×#4111yescharacteristic
735C2×C3C2×C3×H(5,𝔽2)11yescharacteristic
736C2×C3C2×C3×2−1+411yescharacteristic
737D3—22no—
738D3—43no—
739C22—23no—
740C22—23no—
741C22—23no—
742C22—32no—
743C22—61no—
744C22—61no—
745C22—63no—
746C22—63no—
747C22—63no—
748C22C24×C3×D311yescharacteristic
749C4—21no—
750C4—23no—
751C4—23no—
752C4—21no—
753C4—21no—
754C4—32no—
755C4—61no—
756C4—63no—
757C4—63no—
758C4—63no—
759C4—61no—
760C4C2×C3×#23516yes—
761C3—21no—
762C3#8590811yescharacteristic, direct product factor
763C3C3×#352211yescharacteristic, complemented
764C2—43no—
765C2—62no—
766C2—123no—
767C2C22×C3×#23511yescharacteristic
768C2C3×D3×H(5,𝔽2)11yescharacteristic
769C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#520C2
socleC22×C32C25
hypercenterC3×#520D3
hypocenterC3C3×#3522
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
1. C32×#520C2semidirect
2. C3×#5834C2semidirect
3. C3×#5831C2semidirect
4. C3×#5576C2semidirect
5. C3×#5574C2semidirect
6. C3×C4×D3×Q8C2semidirect
7. C3×Q8×Dic6C2semidirect
8. C3×#5561C2semidirect
9. C3×#5559C2semidirect
10. C3×#5551C2semidirect
11. C3×#5548C2semidirect
12. C3×#5534C2semidirect
13. C3×#5528C2semidirect
14. C3×#5511C2semidirect
15. C3×#5507C2semidirect
17. #85908C3direct (N × H)
82. C3×#520D3semidirect
83. C3×#520C2×C3semidirect
85. #5834C2×C3semidirect
86. #5831C2×C3semidirect
87. #5576C2×C3semidirect
88. #5574C2×C3semidirect
89. C4×D3×Q8C2×C3semidirect
90. Q8×Dic6C2×C3semidirect
91. #5561C2×C3semidirect
92. #5559C2×C3semidirect
93. #5551C2×C3semidirect
94. #5548C2×C3semidirect
95. #5534C2×C3semidirect
96. #5528C2×C3semidirect
97. #5511C2×C3semidirect
98. #5507C2×C3semidirect
264. C32×Q8#41semidirect
306. #520C3×D3semidirect
512. C3×Q8#235semidirect
513. C3×Q8C3×#41semidirect
690. C32#3522semidirect
697. Q8C3×#235semidirect
762. C3#85908direct (N × H)
763. C3C3×#3522semidirect

Maximal subgroups

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

subgroupindex
C32×#5202
C3×#58342
C3×#58312
C3×#55762
C3×#55742
C3×C4×D3×Q82
C3×Q8×Dic62
C3×#55612
C3×#55592
C3×#55512
C3×#55482
C3×#55342
C3×#55282
C3×#55112
C3×#55072
C3×#35223
#859083