Finite Group Databasebeta

← C3×#85884 #11909853

Subgroups — C3×#85884 #11909853

Order 1152.

2117 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#519C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C3×Q8×#67C211yesmaximal, characteristic, complemented
4C3×#5583C213yesmaximal, complemented
5C3×#5581C213yesmaximal, complemented
6C3×#5578C213yesmaximal, complemented
7C3×Q8×D12C211yesmaximal, characteristic, complemented
8C3×#5572C211yesmaximal, characteristic, complemented
9C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
10C3×#5569C211yesmaximal, characteristic, complemented
11C3×#5567C213yesmaximal, complemented
12C3×#5533C213yesmaximal, complemented
13C3×#5529C213yesmaximal, complemented
14C3×#5528C213yesmaximal
15C3×#5518C213yesmaximal, complemented
16C3×#3523—31nomaximal
17#85884C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C32×C4×Q8C2213yes—
22C32×C4×Q8C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic
24C32×C4×Q8C2213yes—
25C32×#117C2213yes—
26C32×#117C2213yes—
27C3×#946C2213yes—
28C3×#946C2213yes—
29C3×Q8×Dic3C2211yescharacteristic
30C3×Q8×Dic3C2211yescharacteristic
31C3×#944C2213yes—
32C3×#944C2213yes—
33C3×C4×#67C2213yes—
34C3×C4×#67C2213yes—
35C3×#924C2213yes—
36C3×#924C2213yes—
37C3×#898C2213yes—
38C3×#897C2213yes—
39C3×#897C2213yes—
40C3×#896C2213yes—
41C3×#894C2213yes—
42C3×#892C2213yes—
43C3×D3×C4⋊C4C2213yes—
44C3×#890C2213yes—
45C3×#889C2216yes—
46C3×#889C2216yes—
47C3×#889C2213yes—
48C3×#888C2213yes—
49C3×#887C2213yes—
50C3×#887C2213yes—
51C3×#885C2213yes—
52C3×#884C2211yescharacteristic
53C3×#883C2213yes—
54C3×#879C2213yes—
55C3×#879C2216yes—
56C3×#876C2216yes—
57C3×C4×D12C2213yes—
58C3×#872C2213yes—
59C3×#872C2216yes—
60C3×C42×D3C2213yes—
61C3×#870C2213yes—
62C3×#870C2216yes—
63C3×#869C2213yes—
64C3×C4×Dic6C2213yes—
65C3×C4×Dic6C2213yes—
66C3×C4×Dic6C2213yes—
67C3×C4×Dic6C2216yes—
68C3×#557—33no—
69C3×#557—31no—
70C3×#556—33no—
71C3×#552—33no—
72C3×#552—33no—
73C3×D4×Q8—31no—
74C3×D4×Q8—31no—
75C3×D4×Q8—31no—
76C3×#541—33no—
77C3×#541—33no—
78C3×#533—33no—
79C3×#529—33no—
80C3×#519—21no—
81C3×#519—31no—
82C3×#519D311yescharacteristic, complemented
83C3×#519C2×C311yescharacteristic, complemented
84C2×C3×C4×Q8—31no—
85Q8×#67C2×C311yescharacteristic, complemented
86Q8×#67C2×C311yescharacteristic, complemented
87#5583C2×C313yescomplemented
88#5581C2×C313yescomplemented
89#5578C2×C313yescomplemented
90Q8×D12C2×C311yescharacteristic, complemented
91#5572C2×C311yescharacteristic, complemented
92C4×D3×Q8C2×C311yescharacteristic, complemented
93#5569C2×C311yescharacteristic, complemented
94#5567C2×C313yescomplemented
95#5533C2×C313yescomplemented
96#5529C2×C313yescomplemented
97#5528C2×C313yes—
98#5518C2×C313yescomplemented
99C2×C32×Q8—24no—
100C2×C32×Q8C2313yes—
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4C2313yes—
103C2×C3×#67C2311yescharacteristic
104C2×C3×#67C2311yescharacteristic
105C3×D3×Q8—24no—
106C3×D3×Q8—24no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2313yes—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2313yes—
111C2×C3×C4×D3C2313yes—
112C2×C3×Dic6C2313yes—
113C2×C3×Dic6C2313yes—
114C2×C3×Dic6C2313yes—
115C32×C4⋊C4C2313yes—
116C32×C4⋊C4C2313yes—
117C32×C4⋊C4C2313yes—
118C32×C4⋊C4C2313yes—
119C32×C22⋊C4C2311yescharacteristic
120C32×C22⋊C4C2313yes—
121C32×C42C2313yes—
122C32×C42C2313yes—
123C32×C42C2316yes—
124C3×#217C2313yes—
125C3×#217C2313yes—
126C3×(C2×D3)⋊C4C2313yes—
127C3×(C2×D3)⋊C4C2311yescharacteristic
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2313yes—
130C3×(C2×D3)⋊C4C2313yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×C4⋊Dic3C2313yes—
133C3×C4⋊Dic3C2316yes—
134C3×C4⋊Dic3C2313yes—
135C3×C4⋊Dic3C2313yes—
136C3×C4⋊Dic3C2313yes—
137C3×Dic3⋊C4C2316yes—
138C3×Dic3⋊C4C2316yes—
139C3×Dic3⋊C4C2313yes—
140C3×Dic3⋊C4C2313yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2311yescharacteristic
143C3×Dic3⋊C4C2316yes—
144C3×Dic3⋊C4C2316yes—
145C3×Dic3⋊C4C2313yes—
146C3×Dic3⋊C4C2313yes—
147C3×C4×Dic3C2316yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150C3×C4×Dic3C2313yes—
151C3×C4×Dic3C2313yes—
152#3523—31noSylow
153C22×C3×Q8—21no—
154C22×C3×Q8—31no—
155C22×C3×Q8—31no—
156C22×C3×Q8C2×D311yescharacteristic
157C22×C3×Q8C22×C311yescharacteristic
158C2×D3×Q8C22×C311yescharacteristic
159C2×D3×Q8C22×C311yescharacteristic
160C3×C4⋊Q8—33no—
161C3×C4⋊Q8—33no—
162C3×C4⋊Q8—33no—
163C3×C4⋊Q8—33no—
164C3×#126—33no—
165C3×#126—33no—
166C3×#126—36no—
167C3×#126—36no—
168C3×#125—33no—
169C3×#125—36no—
170C3×#125—36no—
171C3×#125—33no—
172C3×#125—36no—
173C3×#125—33no—
174C3×#124—33no—
175C3×#123—33no—
176C3×#123—33no—
177C3×C22⋊Q8—33no—
178C3×C22⋊Q8—33no—
179C3×C22⋊Q8—33no—
180C3×C22⋊Q8—33no—
181C3×C22⋊Q8—33no—
182C3×C22⋊Q8—33no—
183C3×C22⋊Q8—33no—
184C3×#121—31no—
185C3×C4×Q8—21no—
186C3×C4×Q8—23no—
187C3×C4×Q8—21no—
188C3×C4×Q8—23no—
189C3×C4×Q8—31no—
190C3×C4×Q8—31no—
191C3×C4×Q8—33no—
192C3×C4×Q8—33no—
193C3×C4×Q8—33no—
194C3×C4×Q8—33no—
195C3×C4×Q8—33no—
196C3×C4×Q8—36no—
197C3×C4×Q8C2×D311yescharacteristic
198C3×C4×Q8C2×D313yes—
199C3×C4×Q8C2×D311yescharacteristic
200C3×C4×Q8C2×D313yes—
201C3×C4×Q8C22×C313yes—
202C3×C4×Q8C22×C311yescharacteristic
203C3×C4×Q8C22×C311yescharacteristic
204C3×C4×Q8C22×C313yes—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×C4×D4—33no—
208C3×#117—23no—
209C3×#117—23no—
210C3×#117—33no—
211C3×#117—33no—
212C3×#117—36no—
213C3×#117C2×D313yes—
214C3×#117C2×D313yes—
215C3×#117C22×C313yes—
216C3×#117C22×C313yes—
217C2×C3×C4⋊C4—33no—
218C2×C3×C42—33no—
219#946C22×C313yes—
220#946C22×C313yes—
221Q8×Dic3C22×C311yescharacteristic
222Q8×Dic3C22×C311yescharacteristic
223#944C22×C313yes—
224#944C22×C313yes—
225C4×#67C22×C313yes—
226C4×#67C22×C313yes—
227#924C22×C313yes—
228#924C22×C313yes—
229#898C22×C313yes—
230#897C22×C313yes—
231#897C22×C313yes—
232#896C22×C313yes—
233#894C22×C313yes—
234#892C22×C313yes—
235D3×C4⋊C4C22×C313yes—
236#890C22×C313yes—
237#889C22×C316yes—
238#889C22×C316yes—
239#889C22×C313yes—
240#888C22×C313yes—
241#887C22×C313yes—
242#887C22×C313yes—
243#885C22×C313yes—
244#884C22×C311yescharacteristic
245#883C22×C313yes—
246#879C22×C313yes—
247#879C22×C316yes—
248#876C22×C316yes—
249C4×D12C22×C313yes—
250#872C22×C313yes—
251#872C22×C316yes—
252C42×D3C22×C313yes—
253#870C22×C313yes—
254#870C22×C316yes—
255#869C22×C313yes—
256C4×Dic6C22×C313yes—
257C4×Dic6C22×C313yes—
258C4×Dic6C22×C313yes—
259C4×Dic6C22×C316yes—
260C23×C32C2411yescharacteristic
261C22×C3×D3C2411yescharacteristic
262C22×C3×D3C2411yescharacteristic
263C32×Q8—26no—
264C32×Q8#4114yes—
265C2×C32×C4—26no—
266C2×C32×C4C2413yes—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2413yes—
269C2×C32×C4C2411yescharacteristic
270C2×C32×C4C2413yes—
271C2×C32×C4C2413yes—
272C3×#67—22no—
273C3×#67—22no—
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2413yes—
279C2×C3×Dic3C2411yescharacteristic
280C3×D12—22no—
281C3×C4×D3—26no—
282C3×C4×D3—26no—
283C3×C4×D3—26no—
284C3×C4×D3—22no—
285C3×Dic6—26no—
286C3×Dic6—26no—
287C3×Dic6—26no—
288#557—33no—
289#557—31no—
290#556—33no—
291#552—33no—
292#552—33no—
293D4×Q8—31no—
294D4×Q8—31no—
295D4×Q8—31no—
296#541—33no—
297#541—33no—
298#533—33no—
299#529—33no—
300#519—31no—
301#519C3×D311yescharacteristic, complemented
302C2×C4×Q8—31no—
303C2×C3×Q8—28no—
304C2×C3×Q8—24no—
305C2×C3×Q8—24no—
306C2×C3×Q8—23no—
307C2×C3×Q8—21no—
308C2×C3×Q8—33no—
309C2×C3×Q8—33no—
310C2×C3×Q8—33no—
311C2×C3×Q8—64no—
312C2×C3×Q8—64no—
313C2×C3×Q8C22×D313yes—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C23×C313yes—
316C2×C3×Q8C23×C311yescharacteristic
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C22×C3×C4—23no—
321C22×C3×C4—31no—
322C22×C3×C4—33no—
323C22×C3×C4—33no—
324C22×C3×C4—33no—
325C22×C3×C4C22×D313yes—
326C22×C3×C4C23×C313yes—
327C2×#67C23×C311yescharacteristic
328C2×#67C23×C311yescharacteristic
329D3×Q8—24no—
330D3×Q8—24no—
331C2×D12C23×C311yescharacteristic
332C2×C4×D3C23×C311yescharacteristic
333C2×C4×D3C23×C313yes—
334C2×C4×D3C23×C313yes—
335C2×C4×D3C23×C313yes—
336C2×Dic6C23×C313yes—
337C2×Dic6C23×C313yes—
338C2×Dic6C23×C313yes—
339C3×C4⋊C4—23no—
340C3×C4⋊C4—23no—
341C3×C4⋊C4—23no—
342C3×C4⋊C4—23no—
343C3×C4⋊C4—36no—
344C3×C4⋊C4—33no—
345C3×C4⋊C4—33no—
346C3×C4⋊C4—36no—
347C3×C4⋊C4—36no—
348C3×C4⋊C4—33no—
349C3×C4⋊C4—33no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—36no—
352C3×C4⋊C4—33no—
353C3×C4⋊C4—33no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—36no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4C22×D313yes—
359C3×C4⋊C4C22×D313yes—
360C3×C4⋊C4C22×D313yes—
361C3×C4⋊C4C22×D313yes—
362C3×C4⋊C4C23×C313yes—
363C3×C4⋊C4C23×C313yes—
364C3×C4⋊C4C23×C313yes—
365C3×C4⋊C4C23×C313yes—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—23no—
368C3×C22⋊C4—33no—
369C3×C22⋊C4—33no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—33no—
372C3×C22⋊C4—33no—
373C3×C22⋊C4—33no—
374C3×C22⋊C4—33no—
375C3×C22⋊C4—33no—
376C3×C22⋊C4C22×D311yescharacteristic
377C3×C22⋊C4C22×D313yes—
378C3×C22⋊C4C23×C311yescharacteristic
379C3×C22⋊C4C23×C313yes—
380C3×C42—23no—
381C3×C42—26no—
382C3×C42—23no—
383C3×C42—33no—
384C3×C42—33no—
385C3×C42—33no—
386C3×C42—36no—
387C3×C42—33no—
388C3×C42C22×D313yes—
389C3×C42C22×D316yes—
390C3×C42C22×D313yes—
391C3×C42C23×C313yes—
392C3×C42C23×C313yes—
393C3×C42C23×C316yes—
394#217C23×C313yes—
395#217C23×C313yes—
396(C2×D3)⋊C4C23×C311yescharacteristic
397(C2×D3)⋊C4C23×C313yes—
398(C2×D3)⋊C4C23×C313yes—
399(C2×D3)⋊C4C23×C313yes—
400(C2×D3)⋊C4C23×C313yes—
401(C2×D3)⋊C4C23×C313yes—
402C4⋊Dic3C23×C316yes—
403C4⋊Dic3C23×C313yes—
404C4⋊Dic3C23×C313yes—
405C4⋊Dic3C23×C313yes—
406C4⋊Dic3C23×C313yes—
407Dic3⋊C4C23×C311yescharacteristic
408Dic3⋊C4C23×C313yes—
409Dic3⋊C4C23×C313yes—
410Dic3⋊C4C23×C313yes—
411Dic3⋊C4C23×C316yes—
412Dic3⋊C4C23×C316yes—
413Dic3⋊C4C23×C313yes—
414Dic3⋊C4C23×C313yes—
415Dic3⋊C4C23×C316yes—
416Dic3⋊C4C23×C316yes—
417C4×Dic3C23×C313yes—
418C4×Dic3C23×C313yes—
419C4×Dic3C23×C316yes—
420C4×Dic3C23×C313yes—
421C4×Dic3C23×C313yes—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32C2511yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D32−1+412yes—
432C32×C4—23no—
433C32×C4—23no—
434C32×C4—23no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4C2×#4116yes—
438C3×Dic3—23no—
439C3×Dic3—23no—
440C3×Dic3—23no—
441C3×Dic3—23no—
442C3×Dic3—21no—
443C3×Dic32−1+412yes—
444C22×Q8—31no—
445C22×Q8—31no—
446C22×Q8C2×C3×D311yescharacteristic
447C4⋊Q8—33no—
448C4⋊Q8—33no—
449C4⋊Q8—33no—
450C4⋊Q8—33no—
451#126—33no—
452#126—33no—
453#126—36no—
454#126—36no—
455#125—33no—
456#125—36no—
457#125—36no—
458#125—33no—
459#125—36no—
460#125—33no—
461#124—33no—
462#123—33no—
463#123—33no—
464C22⋊Q8—33no—
465C22⋊Q8—33no—
466C22⋊Q8—33no—
467C22⋊Q8—33no—
468C22⋊Q8—33no—
469C22⋊Q8—33no—
470C22⋊Q8—33no—
471#121—31no—
472C4×Q8—31no—
473C4×Q8—31no—
474C4×Q8—33no—
475C4×Q8—33no—
476C4×Q8—33no—
477C4×Q8—33no—
478C4×Q8—33no—
479C4×Q8—36no—
480C4×Q8C2×C3×D311yescharacteristic
481C4×Q8C2×C3×D313yes—
482C4×Q8C2×C3×D311yescharacteristic
483C4×Q8C2×C3×D313yes—
484C4×D4—33no—
485C4×D4—33no—
486C4×D4—33no—
487#117—33no—
488#117—33no—
489#117—36no—
490#117C2×C3×D313yes—
491#117C2×C3×D313yes—
492C2×C4⋊C4—33no—
493C2×C42—33no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3C23×D311yescharacteristic
498C23×C3C24×C311yescharacteristic
499C22×D3C24×C311yescharacteristic
500C22×D3C24×C311yescharacteristic
501C3×Q8—212no—
502C3×Q8—26no—
503C3×Q8—26no—
504C3×Q8—24no—
505C3×Q8—66no—
506C3×Q8—66no—
507C3×Q8—66no—
508C3×Q8#23514yes—
509C3×Q8C3×#4114yes—
510C3×D4—62no—
511C3×D4—62no—
512C3×D4—62no—
513C2×C3×C4—212no—
514C2×C3×C4—26no—
515C2×C3×C4—26no—
516C2×C3×C4—23no—
517C2×C3×C4—23no—
518C2×C3×C4—23no—
519C2×C3×C4—21no—
520C2×C3×C4—23no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—33no—
524C2×C3×C4—31no—
525C2×C3×C4—33no—
526C2×C3×C4—33no—
527C2×C3×C4—33no—
528C2×C3×C4—62no—
529C2×C3×C4—66no—
530C2×C3×C4—66no—
531C2×C3×C4—66no—
532C2×C3×C4C23×D313yes—
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D313yes—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D313yes—
537C2×C3×C4C23×D313yes—
538C2×C3×C4C24×C311yescharacteristic
539C2×C3×C4C24×C313yes—
540C2×C3×C4C24×C313yes—
541C2×C3×C4C24×C311yescharacteristic
542C2×C3×C4C24×C313yes—
543C2×C3×C4C24×C313yes—
544#67—22no—
545#67—22no—
546C2×Dic3C24×C311yescharacteristic
547C2×Dic3C24×C313yes—
548C2×Dic3C24×C313yes—
549C2×Dic3C24×C313yes—
550C2×Dic3C24×C313yes—
551C2×Dic3C24×C311yescharacteristic
552D12—22no—
553C4×D3—26no—
554C4×D3—26no—
555C4×D3—26no—
556C4×D3—22no—
557Dic6—26no—
558Dic6—26no—
559Dic6—26no—
560C2×C32—41no—
561C2×C32C22×#4111yescharacteristic
562C2×C32C2×2−1+411yescharacteristic
563C2×C32C2×2−1+411yescharacteristic
564C3×D3—22no—
565C3×D3—41no—
566C2×Q8—24no—
567C2×Q8—33no—
568C2×Q8—33no—
569C2×Q8—33no—
570C2×Q8—64no—
571C2×Q8—64no—
572C2×Q8C22×C3×D313yes—
573C2×Q8C22×C3×D311yescharacteristic
574C2×D4—31no—
575C2×D4—31no—
576C2×D4—31no—
577C22×C4—31no—
578C22×C4—33no—
579C22×C4—33no—
580C22×C4—33no—
581C22×C4C22×C3×D313yes—
582C4⋊C4—33no—
583C4⋊C4—36no—
584C4⋊C4—33no—
585C4⋊C4—33no—
586C4⋊C4—33no—
587C4⋊C4—36no—
588C4⋊C4—36no—
589C4⋊C4—33no—
590C4⋊C4—33no—
591C4⋊C4—33no—
592C4⋊C4—31no—
593C4⋊C4—36no—
594C4⋊C4—36no—
595C4⋊C4—33no—
596C4⋊C4—33no—
597C4⋊C4C22×C3×D313yes—
598C4⋊C4C22×C3×D313yes—
599C4⋊C4C22×C3×D313yes—
600C4⋊C4C22×C3×D313yes—
601C22⋊C4—33no—
602C22⋊C4—33no—
603C22⋊C4—31no—
604C22⋊C4—33no—
605C22⋊C4—33no—
606C22⋊C4—33no—
607C22⋊C4—33no—
608C22⋊C4—33no—
609C22⋊C4C22×C3×D311yescharacteristic
610C22⋊C4C22×C3×D313yes—
611C42—33no—
612C42—33no—
613C42—33no—
614C42—36no—
615C42—33no—
616C42C22×C3×D313yes—
617C42C22×C3×D316yes—
618C42C22×C3×D313yes—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—32no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3C24×D311yescharacteristic
636C22×C3C25×C311yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3C3×2−1+412yes—
643C3×C4—26no—
644C3×C4—23no—
645C3×C4—21no—
646C3×C4—23no—
647C3×C4—21no—
648C3×C4—23no—
649C3×C4—23no—
650C3×C4—23no—
651C3×C4—23no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—26no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—43no—
658C3×C4—41no—
659C3×C4—43no—
660C3×C4—63no—
661C3×C4—63no—
662C3×C4—63no—
663C3×C4—61no—
664C3×C4—63no—
665C3×C4C2×#23516yes—
666C3×C4C2×C3×#4116yes—
667Dic3—23no—
668Dic3—23no—
669Dic3—23no—
670Dic3—23no—
671Dic3—21no—
672Dic3C3×2−1+412yes—
673C32#352311yescharacteristic, complemented, Sylow
674C23—31no—
675C23—31no—
676C23C23×C3×D311yescharacteristic
677Q8—26no—
678Q8—66no—
679Q8—66no—
680Q8—66no—
681Q8C3×#23514yes—
682D4—62no—
683D4—62no—
684D4—62no—
685C2×C4—26no—
686C2×C4—31no—
687C2×C4—33no—
688C2×C4—31no—
689C2×C4—33no—
690C2×C4—33no—
691C2×C4—33no—
692C2×C4—62no—
693C2×C4—66no—
694C2×C4—66no—
695C2×C4—66no—
696C2×C4C23×C3×D313yes—
697C2×C4C23×C3×D311yescharacteristic
698C2×C4C23×C3×D313yes—
699C2×C4C23×C3×D311yescharacteristic
700C2×C4C23×C3×D313yes—
701C2×C4C23×C3×D313yes—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—42no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—62no—
709C2×C3—121no—
710C2×C3C22×#23511yescharacteristic
711C2×C3D3×2−1+411yescharacteristic
712C2×C3D3×2−1+411yescharacteristic
713C2×C3C22×C3×#4111yescharacteristic
714C2×C3C2×C3×2−1+411yescharacteristic
715C2×C3C2×C3×2−1+411yescharacteristic
716D3—22no—
717D3—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—32no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22C24×C3×D311yescharacteristic
728C4—23no—
729C4—21no—
730C4—23no—
731C4—21no—
732C4—23no—
733C4—32no—
734C4—63no—
735C4—63no—
736C4—63no—
737C4—61no—
738C4—63no—
739C4C2×C3×#23516yes—
740C3—21no—
741C3#8588411yescharacteristic, direct product factor
742C3C3×#352311yescharacteristic, complemented
743C2—41no—
744C2—62no—
745C2—121no—
746C2C22×C3×#23511yescharacteristic
747C2C3×D3×2−1+411yescharacteristic
748C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#519C2
socleC22×C32C25
prime radicalC3×#884C22
hypercenterC3×#519D3
hypocenterC3C3×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#519

Complements

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

NH ≅ G/Ntype
1. C32×#519C2semidirect
2. C3×Q8×#67C2semidirect
3. C3×Q8×#67C2semidirect
4. C3×#5583C2semidirect
5. C3×#5581C2semidirect
6. C3×#5578C2semidirect
7. C3×Q8×D12C2semidirect
8. C3×#5572C2semidirect
9. C3×C4×D3×Q8C2semidirect
10. C3×#5569C2semidirect
11. C3×#5567C2semidirect
12. C3×#5533C2semidirect
13. C3×#5529C2semidirect
15. C3×#5518C2semidirect
17. #85884C3direct (N × H)
82. C3×#519D3semidirect
83. C3×#519C2×C3semidirect
85. Q8×#67C2×C3semidirect
86. Q8×#67C2×C3semidirect
87. #5583C2×C3semidirect
88. #5581C2×C3semidirect
89. #5578C2×C3semidirect
90. Q8×D12C2×C3semidirect
91. #5572C2×C3semidirect
92. C4×D3×Q8C2×C3semidirect
93. #5569C2×C3semidirect
94. #5567C2×C3semidirect
95. #5533C2×C3semidirect
96. #5529C2×C3semidirect
98. #5518C2×C3semidirect
301. #519C3×D3semidirect
673. C32#3523semidirect
741. C3#85884direct (N × H)
742. C3C3×#3523semidirect

Maximal subgroups

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

subgroupindex
C32×#5192
C3×Q8×#672
C3×#55832
C3×#55812
C3×#55782
C3×Q8×D122
C3×#55722
C3×C4×D3×Q82
C3×#55692
C3×#55672
C3×#55332
C3×#55292
C3×#55282
C3×#55182
C3×#35233
#858843