Finite Group Databasebeta

← C3×#87032 #11906259

Subgroups — C3×#87032 #11906259

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5729C213yesmaximal
3C3×#5722C213yesmaximal, complemented
4C3×#5689C213yesmaximal
5C3×#5688C213yesmaximal
6C3×#5685C213yesmaximal, complemented
7C3×#5685C213yesmaximal, complemented
8C3×#5578C213yesmaximal
9C3×#5572C211yesmaximal, characteristic
10C3×#5572C211yesmaximal, characteristic
11C3×C4×D3×Q8C211yesmaximal, characteristic
12C3×#5569C211yesmaximal, characteristic, complemented
13C3×#5569C211yesmaximal, characteristic, complemented
14C3×#5567C213yesmaximal, complemented
15C3×Q8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3502—31nomaximal
17#87032C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C32×C4⋊Q8C2213yes—
20C32×#125C2213yes—
21C32×#125C2213yes—
22C32×C4×Q8C2211yescharacteristic
23C32×C4×Q8C2213yes—
24C32×C4×Q8C2211yescharacteristic
25C32×C4×Q8C2211yescharacteristic
26C3×#946C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#944C2216yes—
31C3×#944C2213yes—
32C3×#897C2213yes—
33C3×#896C2211yescharacteristic
34C3×#896C2213yes—
35C3×#896C2216yes—
36C3×#892C2213yes—
37C3×#892C2213yes—
38C3×D3×C4⋊C4C2213yes—
39C3×#890C2213yes—
40C3×#890C2213yes—
41C3×#889C2213yes—
42C3×#889C2216yes—
43C3×#889C2213yes—
44C3×#889C2216yes—
45C3×#888C2213yes—
46C3×#888C2213yes—
47C3×#888C2213yes—
48C3×#888C2213yes—
49C3×#888C2213yes—
50C3×#888C2216yes—
51C3×#887C2216yes—
52C3×#887C2213yes—
53C3×#887C2213yes—
54C3×#887C2213yes—
55C3×#887C2216yes—
56C3×#872C2213yes—
57C3×#872C2213yes—
58C3×C42×D3C2213yes—
59C3×#870C2213yes—
60C3×#870C2213yes—
61C3×#869C2213yes—
62C3×C4×Dic6C2213yes—
63C3×C4×Dic6C2213yes—
64C3×C4×Dic6C2213yes—
65C3×C4×Dic6C2213yes—
66C3×C4×Dic6C2213yes—
67C3×C4×Dic6C2213yes—
68C3×Q82—33no—
69C3×Q82—31no—
70C3×#557—21no—
71C3×#557—33no—
72C3×#557—33no—
73C3×#557—33no—
74C3×#557—31no—
75C3×#557—31no—
76C3×#557D311yescharacteristic, complemented
77C3×#557C2×C311yescharacteristic, complemented
78C3×#544—33no—
79C3×#544—33no—
80C3×#533—33no—
81C3×#533—33no—
82C3×#519—31no—
83C3×#519—31no—
84C2×C3×C4×Q8—31no—
85#5729C2×C313yes—
86#5722C2×C313yescomplemented
87#5689C2×C313yes—
88#5688C2×C313yes—
89#5685C2×C313yescomplemented
90#5685C2×C313yescomplemented
91#5578C2×C313yes—
92#5572C2×C311yescharacteristic
93#5572C2×C311yescharacteristic
94C4×D3×Q8C2×C311yescharacteristic
95#5569C2×C311yescharacteristic, complemented
96#5569C2×C311yescharacteristic, complemented
97#5567C2×C313yescomplemented
98Q8×Dic6C2×C311yescharacteristic, complemented
99C2×C32×Q8C2313yes—
100C2×C32×Q8C2311yescharacteristic
101C3×D3×Q8Q818yescomplemented
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2313yes—
104C2×C3×C4×D3C2313yes—
105C2×C3×Dic6C2313yes—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2316yes—
108C2×C3×Dic6C2313yes—
109C2×C3×Dic6C2313yes—
110C32×C4⋊C4C2313yes—
111C32×C4⋊C4C2313yes—
112C32×C4⋊C4C2316yes—
113C32×C4⋊C4C2313yes—
114C32×C4⋊C4C2313yes—
115C32×C4⋊C4C2313yes—
116C32×C4⋊C4C2311yescharacteristic
117C32×C42C2313yes—
118C32×C42C2313yes—
119C32×C42C2313yes—
120C3×(C2×D3)⋊C4C2313yes—
121C3×(C2×D3)⋊C4C2313yes—
122C3×(C2×D3)⋊C4C2311yescharacteristic
123C3×(C2×D3)⋊C4C2311yescharacteristic
124C3×C4⋊Dic3C2313yes—
125C3×C4⋊Dic3C2313yes—
126C3×C4⋊Dic3C2313yes—
127C3×C4⋊Dic3C2313yes—
128C3×C4⋊Dic3C2313yes—
129C3×C4⋊Dic3C2313yes—
130C3×Dic3⋊C4C2313yes—
131C3×Dic3⋊C4C2313yes—
132C3×Dic3⋊C4C2313yes—
133C3×Dic3⋊C4C2313yes—
134C3×Dic3⋊C4C2316yes—
135C3×Dic3⋊C4C2316yes—
136C3×Dic3⋊C4C2316yes—
137C3×Dic3⋊C4C2313yes—
138C3×Dic3⋊C4C2313yes—
139C3×Dic3⋊C4C2311yescharacteristic
140C3×Dic3⋊C4C2313yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2311yescharacteristic
143C3×C4×Dic3C2313yes—
144C3×C4×Dic3C2316yes—
145C3×C4×Dic3C2316yes—
146C3×C4×Dic3C2313yes—
147C3×C4×Dic3C2313yes—
148C3×C4×Dic3C2313yes—
149C3×C4×Dic3C2313yes—
150#3502—31noSylow
151C22×C3×Q8—31no—
152C2×D3×Q8C22×C311yescharacteristic
153C3×C4⋊Q8—23no—
154C3×C4⋊Q8—33no—
155C3×C4⋊Q8—36no—
156C3×C4⋊Q8—33no—
157C3×C4⋊Q8—36no—
158C3×C4⋊Q8—33no—
159C3×C4⋊Q8—33no—
160C3×C4⋊Q8—33no—
161C3×C4⋊Q8—33no—
162C3×C4⋊Q8—33no—
163C3×C4⋊Q8C2×D313yes—
164C3×C4⋊Q8C22×C313yes—
165C3×#125—23no—
166C3×#125—23no—
167C3×#125—33no—
168C3×#125—33no—
169C3×#125—36no—
170C3×#125—36no—
171C3×#125—33no—
172C3×#125—33no—
173C3×#125—33no—
174C3×#125—33no—
175C3×#125C2×D313yes—
176C3×#125C2×D313yes—
177C3×#125C22×C313yes—
178C3×#125C22×C313yes—
179C3×C22⋊Q8—33no—
180C3×C22⋊Q8—33no—
181C3×C22⋊Q8—31no—
182C3×C22⋊Q8—36no—
183C3×C22⋊Q8—33no—
184C3×C4×Q8—21no—
185C3×C4×Q8—21no—
186C3×C4×Q8—21no—
187C3×C4×Q8—23no—
188C3×C4×Q8—31no—
189C3×C4×Q8—31no—
190C3×C4×Q8—31no—
191C3×C4×Q8—33no—
192C3×C4×Q8—33no—
193C3×C4×Q8—36no—
194C3×C4×Q8—33no—
195C3×C4×Q8—36no—
196C3×C4×Q8—33no—
197C3×C4×Q8—33no—
198C3×C4×Q8—33no—
199C3×C4×Q8—33no—
200C3×C4×Q8—33no—
201C3×C4×Q8—33no—
202C3×C4×Q8C2×D311yescharacteristic
203C3×C4×Q8C2×D311yescharacteristic
204C3×C4×Q8C2×D311yescharacteristic
205C3×C4×Q8C2×D313yes—
206C3×C4×Q8C22×C311yescharacteristic
207C3×C4×Q8C22×C313yes—
208C3×C4×Q8C22×C311yescharacteristic
209C3×C4×Q8C22×C311yescharacteristic
210C3×#117—33no—
211C3×#117—33no—
212C3×#117—33no—
213C3×#117—33no—
214C2×C3×C4⋊C4—33no—
215C2×C3×C42—33no—
216#946C22×C313yes—
217Q8×Dic3C22×C311yescharacteristic
218Q8×Dic3C22×C311yescharacteristic
219Q8×Dic3C22×C311yescharacteristic
220#944C22×C313yes—
221#944C22×C316yes—
222#897C22×C313yes—
223#896C22×C313yes—
224#896C22×C316yes—
225#896C22×C311yescharacteristic
226#892C22×C313yes—
227#892C22×C313yes—
228D3×C4⋊C4C22×C313yes—
229#890C22×C313yes—
230#890C22×C313yes—
231#889C22×C316yes—
232#889C22×C313yes—
233#889C22×C316yes—
234#889C22×C313yes—
235#888C22×C313yes—
236#888C22×C313yes—
237#888C22×C316yes—
238#888C22×C313yes—
239#888C22×C313yes—
240#888C22×C313yes—
241#887C22×C313yes—
242#887C22×C316yes—
243#887C22×C316yes—
244#887C22×C313yes—
245#887C22×C313yes—
246#872C22×C313yes—
247#872C22×C313yes—
248C42×D3C22×C313yes—
249#870C22×C313yes—
250#870C22×C313yes—
251#869C22×C313yes—
252C4×Dic6C22×C313yes—
253C4×Dic6C22×C313yes—
254C4×Dic6C22×C313yes—
255C4×Dic6C22×C313yes—
256C4×Dic6C22×C313yes—
257C4×Dic6C22×C313yes—
258C22×C3×D3C2411yescharacteristic
259C32×Q8—43no—
260C32×Q8C2×Q814yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2413yes—
263C2×C32×C4C2413yes—
264C2×C32×C4C2413yes—
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2413yes—
268C2×C3×Dic3C2413yes—
269C2×C3×Dic3C2411yescharacteristic
270C2×C3×Dic3C2413yes—
271C2×C3×Dic3C2411yescharacteristic
272C2×C3×Dic3C2413yes—
273C2×C3×Dic3C2413yes—
274C2×C3×Dic3C2411yescharacteristic
275C3×C4×D3—22no—
276C3×C4×D3—43no—
277C3×C4×D3C2×Q8112yes—
278C3×Dic6—26no—
279C3×Dic6—22no—
280C3×Dic6—43no—
281C3×Dic6—46no—
282C3×Dic6C2×Q8112yes—
283Q82—33no—
284Q82—31no—
285#557—33no—
286#557—33no—
287#557—33no—
288#557—31no—
289#557—31no—
290#557C3×D311yescharacteristic, complemented
291#544—33no—
292#544—33no—
293#533—33no—
294#533—33no—
295#519—31no—
296#519—31no—
297C2×C4×Q8—31no—
298C2×C3×Q8—21no—
299C2×C3×Q8—23no—
300C2×C3×Q8—38no—
301C2×C3×Q8—33no—
302C2×C3×Q8—33no—
303C2×C3×Q8—31no—
304C2×C3×Q8—33no—
305C2×C3×Q8—36no—
306C2×C3×Q8C22×D313yes—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C23×C313yes—
309C2×C3×Q8C23×C311yescharacteristic
310C22×C3×C4—33no—
311C22×C3×C4—31no—
312C22×C3×C4—33no—
313D3×Q8C3×Q818yescomplemented
314C2×C4×D3C23×C311yescharacteristic
315C2×C4×D3C23×C313yes—
316C2×C4×D3C23×C313yes—
317C2×Dic6C23×C311yescharacteristic
318C2×Dic6C23×C313yes—
319C2×Dic6C23×C313yes—
320C2×Dic6C23×C316yes—
321C2×Dic6C23×C313yes—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—23no—
324C3×C4⋊C4—23no—
325C3×C4⋊C4—23no—
326C3×C4⋊C4—23no—
327C3×C4⋊C4—23no—
328C3×C4⋊C4—26no—
329C3×C4⋊C4—36no—
330C3×C4⋊C4—33no—
331C3×C4⋊C4—33no—
332C3×C4⋊C4—33no—
333C3×C4⋊C4—33no—
334C3×C4⋊C4—33no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—33no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—36no—
339C3×C4⋊C4—36no—
340C3×C4⋊C4—33no—
341C3×C4⋊C4—33no—
342C3×C4⋊C4—33no—
343C3×C4⋊C4—33no—
344C3×C4⋊C4—33no—
345C3×C4⋊C4—33no—
346C3×C4⋊C4—33no—
347C3×C4⋊C4—33no—
348C3×C4⋊C4C22×D313yes—
349C3×C4⋊C4C22×D313yes—
350C3×C4⋊C4C22×D313yes—
351C3×C4⋊C4C22×D313yes—
352C3×C4⋊C4C22×D316yes—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D313yes—
355C3×C4⋊C4C23×C313yes—
356C3×C4⋊C4C23×C313yes—
357C3×C4⋊C4C23×C316yes—
358C3×C4⋊C4C23×C313yes—
359C3×C4⋊C4C23×C313yes—
360C3×C4⋊C4C23×C313yes—
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—33no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—33no—
365C3×C22⋊C4—31no—
366C3×C42—23no—
367C3×C42—23no—
368C3×C42—23no—
369C3×C42—33no—
370C3×C42—33no—
371C3×C42—33no—
372C3×C42—36no—
373C3×C42—36no—
374C3×C42—33no—
375C3×C42—33no—
376C3×C42C22×D313yes—
377C3×C42C22×D313yes—
378C3×C42C22×D313yes—
379C3×C42C23×C313yes—
380C3×C42C23×C313yes—
381C3×C42C23×C313yes—
382(C2×D3)⋊C4C23×C311yescharacteristic
383(C2×D3)⋊C4C23×C311yescharacteristic
384(C2×D3)⋊C4C23×C313yes—
385(C2×D3)⋊C4C23×C313yes—
386C4⋊Dic3C23×C313yes—
387C4⋊Dic3C23×C313yes—
388C4⋊Dic3C23×C313yes—
389C4⋊Dic3C23×C313yes—
390C4⋊Dic3C23×C313yes—
391C4⋊Dic3C23×C313yes—
392Dic3⋊C4C23×C311yescharacteristic
393Dic3⋊C4C23×C311yescharacteristic
394Dic3⋊C4C23×C313yes—
395Dic3⋊C4C23×C313yes—
396Dic3⋊C4C23×C313yes—
397Dic3⋊C4C23×C313yes—
398Dic3⋊C4C23×C313yes—
399Dic3⋊C4C23×C316yes—
400Dic3⋊C4C23×C313yes—
401Dic3⋊C4C23×C316yes—
402Dic3⋊C4C23×C316yes—
403Dic3⋊C4C23×C313yes—
404Dic3⋊C4C23×C313yes—
405C4×Dic3C23×C313yes—
406C4×Dic3C23×C313yes—
407C4×Dic3C23×C313yes—
408C4×Dic3C23×C313yes—
409C4×Dic3C23×C316yes—
410C4×Dic3C23×C316yes—
411C4×Dic3C23×C313yes—
412C22×C32C2511yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C22×Q812yes—
416C32×C4—21no—
417C32×C4—23no—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—23no—
421C32×C4—23no—
422C32×C4C22×Q816yes—
423C3×Dic3—23no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—23no—
427C3×Dic3—23no—
428C3×Dic3C22×Q816yes—
429C3×Dic32−1+412yes—
430C22×Q8—31no—
431C4⋊Q8—33no—
432C4⋊Q8—36no—
433C4⋊Q8—33no—
434C4⋊Q8—33no—
435C4⋊Q8—33no—
436C4⋊Q8—36no—
437C4⋊Q8—33no—
438C4⋊Q8—33no—
439C4⋊Q8—33no—
440C4⋊Q8C2×C3×D313yes—
441#125—33no—
442#125—33no—
443#125—36no—
444#125—36no—
445#125—33no—
446#125—33no—
447#125—33no—
448#125—33no—
449#125C2×C3×D313yes—
450#125C2×C3×D313yes—
451C22⋊Q8—33no—
452C22⋊Q8—33no—
453C22⋊Q8—31no—
454C22⋊Q8—36no—
455C22⋊Q8—33no—
456C4×Q8—31no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—33no—
460C4×Q8—33no—
461C4×Q8—33no—
462C4×Q8—36no—
463C4×Q8—36no—
464C4×Q8—33no—
465C4×Q8—33no—
466C4×Q8—33no—
467C4×Q8—33no—
468C4×Q8—33no—
469C4×Q8—33no—
470C4×Q8C2×C3×D311yescharacteristic
471C4×Q8C2×C3×D311yescharacteristic
472C4×Q8C2×C3×D311yescharacteristic
473C4×Q8C2×C3×D313yes—
474#117—33no—
475#117—33no—
476#117—33no—
477#117—33no—
478C2×C4⋊C4—33no—
479C2×C42—33no—
480C23×C3—31no—
481C22×D3C24×C311yescharacteristic
482C3×Q8—24no—
483C3×Q8—312no—
484C3×Q8—43no—
485C3×Q8—43no—
486C3×Q8—46no—
487C3×Q8—66no—
488C3×Q8—62no—
489C3×Q8—123no—
490C3×Q8—126no—
491C3×Q8D3×Q814yes—
492C3×Q8C2×C3×Q814yes—
493C2×C3×C4—23no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—23no—
498C2×C3×C4—23no—
499C2×C3×C4—23no—
500C2×C3×C4—33no—
501C2×C3×C4—31no—
502C2×C3×C4—312no—
503C2×C3×C4—31no—
504C2×C3×C4—33no—
505C2×C3×C4—31no—
506C2×C3×C4—33no—
507C2×C3×C4—33no—
508C2×C3×C4—62no—
509C2×C3×C4—123no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D313yes—
512C2×C3×C4C23×D313yes—
513C2×C3×C4C23×D313yes—
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D313yes—
517C2×C3×C4C24×C311yescharacteristic
518C2×C3×C4C24×C313yes—
519C2×C3×C4C24×C313yes—
520C2×C3×C4C24×C313yes—
521C2×C3×C4C24×C311yescharacteristic
522C2×C3×C4C24×C311yescharacteristic
523C2×C3×C4C24×C313yes—
524C2×Dic3C24×C311yescharacteristic
525C2×Dic3C24×C313yes—
526C2×Dic3C24×C311yescharacteristic
527C2×Dic3C24×C313yes—
528C2×Dic3C24×C313yes—
529C2×Dic3C24×C313yes—
530C2×Dic3C24×C311yescharacteristic
531C4×D3—22no—
532C4×D3—43no—
533C4×D3C2×C3×Q8112yes—
534Dic6—22no—
535Dic6—26no—
536Dic6—43no—
537Dic6—46no—
538Dic6C2×C3×Q8112yes—
539C2×C32C23×Q811yescharacteristic
540C2×C32C2×2−1+411yescharacteristic
541C2×C32#58511yescharacteristic
542C3×D3—22no—
543C2×Q8—38no—
544C2×Q8—33no—
545C2×Q8—33no—
546C2×Q8—31no—
547C2×Q8—33no—
548C2×Q8—36no—
549C2×Q8C22×C3×D313yes—
550C2×Q8C22×C3×D311yescharacteristic
551C22×C4—33no—
552C22×C4—31no—
553C22×C4—33no—
554C4⋊C4—36no—
555C4⋊C4—33no—
556C4⋊C4—33no—
557C4⋊C4—33no—
558C4⋊C4—33no—
559C4⋊C4—33no—
560C4⋊C4—33no—
561C4⋊C4—33no—
562C4⋊C4—33no—
563C4⋊C4—31no—
564C4⋊C4—33no—
565C4⋊C4—31no—
566C4⋊C4—36no—
567C4⋊C4—33no—
568C4⋊C4—36no—
569C4⋊C4—33no—
570C4⋊C4—33no—
571C4⋊C4—33no—
572C4⋊C4—33no—
573C4⋊C4C22×C3×D313yes—
574C4⋊C4C22×C3×D313yes—
575C4⋊C4C22×C3×D313yes—
576C4⋊C4C22×C3×D313yes—
577C4⋊C4C22×C3×D316yes—
578C4⋊C4C22×C3×D311yescharacteristic
579C4⋊C4C22×C3×D313yes—
580C22⋊C4—33no—
581C22⋊C4—31no—
582C22⋊C4—33no—
583C22⋊C4—31no—
584C42—33no—
585C42—33no—
586C42—33no—
587C42—36no—
588C42—36no—
589C42—33no—
590C42—33no—
591C42C22×C3×D313yes—
592C42C22×C3×D313yes—
593C42C22×C3×D313yes—
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3C24×D311yescharacteristic
599C22×C3C25×C311yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3C22×C3×Q812yes—
603C3×C4—22no—
604C3×C4—23no—
605C3×C4—21no—
606C3×C4—23no—
607C3×C4—21no—
608C3×C4—23no—
609C3×C4—21no—
610C3×C4—23no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—23no—
614C3×C4—23no—
615C3×C4—21no—
616C3×C4—26no—
617C3×C4—36no—
618C3×C4—32no—
619C3×C4—43no—
620C3×C4—43no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—43no—
624C3×C4—63no—
625C3×C4—61no—
626C3×C4—63no—
627C3×C4—61no—
628C3×C4—63no—
629C3×C4C2×D3×Q816yes—
630C3×C4C22×C3×Q816yes—
631Dic3—21no—
632Dic3—23no—
633Dic3—21no—
634Dic3—23no—
635Dic3—23no—
636Dic3C22×C3×Q816yes—
637Dic3C3×2−1+412yes—
638C32#350211yescharacteristic, complemented, Sylow
639C23—31no—
640Q8—312no—
641Q8—43no—
642Q8—66no—
643Q8—62no—
644Q8—123no—
645Q8—126no—
646Q8C3×D3×Q814yes—
647C2×C4—33no—
648C2×C4—31no—
649C2×C4—312no—
650C2×C4—31no—
651C2×C4—33no—
652C2×C4—31no—
653C2×C4—33no—
654C2×C4—33no—
655C2×C4—62no—
656C2×C4—123no—
657C2×C4C23×C3×D311yescharacteristic
658C2×C4C23×C3×D313yes—
659C2×C4C23×C3×D313yes—
660C2×C4C23×C3×D313yes—
661C2×C4C23×C3×D311yescharacteristic
662C2×C4C23×C3×D311yescharacteristic
663C2×C4C23×C3×D313yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—62no—
668C2×C3C22×D3×Q811yescharacteristic
669C2×C3#596411yescharacteristic
670C2×C3D3×2−1+411yescharacteristic
671C2×C3C23×C3×Q811yescharacteristic
672C2×C3C2×C3×2−1+411yescharacteristic
673C2×C3C3×#58511yescharacteristic
674D3—22no—
675C22—32no—
676C22—61no—
677C22—61no—
678C22C24×C3×D311yescharacteristic
679C4—23no—
680C4—21no—
681C4—23no—
682C4—21no—
683C4—23no—
684C4—21no—
685C4—36no—
686C4—32no—
687C4—63no—
688C4—61no—
689C4—63no—
690C4—61no—
691C4—63no—
692C4C2×C3×D3×Q816yes—
693C3—21no—
694C3#8703211yescharacteristic, direct product factor
695C3C3×#350211yescharacteristic, complemented
696C2—62no—
697C2C22×C3×D3×Q811yescharacteristic
698C2C3×#596411yescharacteristic
699C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#557C2
socleC22×C32C25
prime radicalC22×C3×D3C24
hypercenterC3×#557D3
hypocenterC3C3×#3502
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5722C2semidirect
6. C3×#5685C2semidirect
7. C3×#5685C2semidirect
12. C3×#5569C2semidirect
13. C3×#5569C2semidirect
14. C3×#5567C2semidirect
15. C3×Q8×Dic6C2semidirect
17. #87032C3direct (N × H)
76. C3×#557D3semidirect
77. C3×#557C2×C3semidirect
86. #5722C2×C3semidirect
89. #5685C2×C3semidirect
90. #5685C2×C3semidirect
95. #5569C2×C3semidirect
96. #5569C2×C3semidirect
97. #5567C2×C3semidirect
98. Q8×Dic6C2×C3semidirect
101. C3×D3×Q8Q8semidirect
290. #557C3×D3semidirect
313. D3×Q8C3×Q8semidirect
638. C32#3502semidirect
694. C3#87032direct (N × H)
695. C3C3×#3502semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
C3×#57292
C3×#57222
C3×#56892
C3×#56882
C3×#56852
C3×#55782
C3×#55722
C3×C4×D3×Q82
C3×#55692
C3×#55672
C3×Q8×Dic62
C3×#35023
#870323