Finite Group Databasebeta

← C3×#63045 #10681652

Subgroups — C3×#63045 #10681652

Order 768.

7484 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3558C216yesmaximal, complemented
2C3×#3558C2112yesmaximal, complemented
3C3×#3549C213yesmaximal, complemented
4C3×#3545C216yesmaximal, complemented
5C3×#3540C216yesmaximal, complemented
6C3×#3532C2112yesmaximal, complemented
7C3×#3529C211yesmaximal, characteristic, complemented
8C2×C3×H(3,𝔽4)C212yesmaximal, complemented
9C3×#3514C216yesmaximal, complemented
10C3×#3500C213yesmaximal, complemented
11C3×#3484C216yesmaximal, complemented
12#63045C311yesmaximal, characteristic, direct product factor, Sylow
13C2×C3×2−1+4C2211yescharacteristic, complemented
14C2×C3×H(5,𝔽2)C2213yescomplemented
15C23×C3×D4C2212yescomplemented
16C3×#563C2213yescomplemented
17C3×#562C2216yescomplemented
18C3×#562C22112yescomplemented
19C3×H(3,𝔽4)C2211yescharacteristic, complemented
20C3×H(3,𝔽4)C22112yescomplemented
21C3×H(3,𝔽4)C2216yescomplemented
22C3×H(3,𝔽4)C22112yescomplemented
23C3×H(3,𝔽4)C2216yescomplemented
24C3×#560C2216yescomplemented
25C3×#560C22112yescomplemented
26C3×#559C2216yescomplemented
27C3×#559C22112yescomplemented
28C3×#556C2216yescomplemented
29C3×#555C22112yescomplemented
30C3×#555C2216yescomplemented
31C3×#551C22112yescomplemented
32C3×#551C22124yescomplemented
33C3×D4×Q8C2212yescomplemented
34C3×#548C22112yescomplemented
35C3×#548C22112yescomplemented
36C3×#546C22112yescomplemented
37C3×#546C22112yescomplemented
38C3×#546C22124yescomplemented
39C3×#546C22112yescomplemented
40C3×#546C22124yescomplemented
41C3×#546C22124yescomplemented
42C3×D42C2216yescomplemented
43C3×D42C22124yescomplemented
44C3×D42C2216yescomplemented
45C3×D42C22112yescomplemented
46C3×#542C22112yescomplemented
47C3×#542C22124yescomplemented
48C3×#538C22124yescomplemented
49C3×#538C22124yescomplemented
50C3×#538C22124yescomplemented
51C3×#538C22112yescomplemented
52C3×#536C2213yescomplemented
53C3×#536C2216yescomplemented
54C3×#535C2216yescomplemented
55C3×#535C2216yescomplemented
56C3×#535C2216yescomplemented
57C3×#535C22124yescomplemented
58C3×#535C2213yescomplemented
59C3×#534C22112yescomplemented
60C3×#534C22112yescomplemented
61C3×#534C22112yescomplemented
62C3×#532C2213yescomplemented
63C3×#532C2216yescomplemented
64C3×#532C2216yescomplemented
65C3×#529C2216yescomplemented
66C3×#529C22112yescomplemented
67C2×C3×#124C2216yescomplemented
68C2×C3×#124C22112yescomplemented
69C2×C3×#124C2213yescomplemented
70C3×#525C2216yescomplemented
71C3×#525C2216yescomplemented
72C2×C3×#120C22112yescomplemented
73C2×C3×#120C22112yescomplemented
74C3×#518C2216yescomplemented
75C3×C4×#41C2213yescomplemented
76#3558C2×C3112yescomplemented
77#3558C2×C316yescomplemented
78#3549C2×C313yescomplemented
79#3545C2×C316yescomplemented
80#3540C2×C316yescomplemented
81#3532C2×C3112yescomplemented
82#3529C2×C311yescharacteristic, complemented
83C2×H(3,𝔽4)C2×C312yescomplemented
84#3514C2×C316yescomplemented
85#3500C2×C313yescomplemented
86#3484C2×C316yescomplemented
87C25×C3C2314yescomplemented
88C3×2−1+4—44no—
89C3×H(5,𝔽2)—412no—
90C2×C3×#41C2313yes—
91C2×C3×#41C2313yes—
92C2×C3×#41C2316yes—
93C2×C3×#41C2316yes—
94C2×C3×#41C2311yescharacteristic, complemented
95C2×C3×#41C2316yescomplemented
96C2×C3×#41C23112yescomplemented
97C22×C3×Q8C2312yescomplemented
98C22×C3×Q8C2313yescomplemented
99C22×C3×Q8C2314yescomplemented
100C22×C3×D4—48no—
101C22×C3×D4C2316yes—
102C22×C3×D4C2316yes—
103C22×C3×D4C23112yes—
104C22×C3×D4C2313yes—
105C22×C3×D4C23112yes—
106C22×C3×D4C23112yescomplemented
107C22×C3×D4C2316yescomplemented
108C22×C3×D4C23124yescomplemented
109C23×C3×C4C2312yescomplemented
110C3×C4⋊Q8C2313yescomplemented
111C3×C4⋊Q8C2316yescomplemented
112C3×C4⋊Q8C2316yescomplemented
113C3×#127C23112yes—
114C3×#127C2316yes—
115C3×#127C2313yes—
116C3×#127C2316yescomplemented
117C3×#126C23112yescomplemented
118C3×#126C23124yescomplemented
119C3×#126C23124yescomplemented
120C3×#125C2316yescomplemented
121C3×#124C2316yes—
122C3×#124C2313yes—
123C3×#124C2316yes—
124C3×#124C23112yes—
125C3×#124C23112yescomplemented
126C3×#124C23124yescomplemented
127C3×#124C23124yescomplemented
128C3×#124C23112yescomplemented
129C3×#124C23112yescomplemented
130C3×#124C2316yescomplemented
131C3×#124C2313yescomplemented
132C3×#124C2316yescomplemented
133C3×#124C23124yescomplemented
134C3×#124C23124yescomplemented
135C3×#124C23112yescomplemented
136C3×#124C2316yescomplemented
137C3×#123C2316yes—
138C3×#123C2316yescomplemented
139C3×#123C23112yescomplemented
140C3×#123C23124yescomplemented
141C3×#123C23124yescomplemented
142C3×#123C23112yescomplemented
143C3×#123C23124yescomplemented
144C3×#123C23112yescomplemented
145C3×#123C23124yescomplemented
146C3×C22⋊Q8C2316yescomplemented
147C3×C22⋊Q8C23112yescomplemented
148C3×C22⋊Q8C23124yescomplemented
149C3×C22⋊Q8C23124yescomplemented
150C3×C22⋊Q8C23112yescomplemented
151C3×C22⋊Q8C23112yescomplemented
152C3×#121C2316yes—
153C3×#121C23112yes—
154C3×#121C23124yes—
155C3×#121C23112yes—
156C3×#121C23112yes—
157C3×#121C23112yescomplemented
158C3×#121C23124yescomplemented
159C3×#121C23124yescomplemented
160C3×#121C23124yescomplemented
161C3×#121C23124yescomplemented
162C3×#121C23112yescomplemented
163C3×#121C23124yescomplemented
164C3×#121C23112yescomplemented
165C3×#120C2316yes—
166C3×#120C23112yes—
167C3×#120C23124yes—
168C3×#120C23124yes—
169C3×#120C2316yescomplemented
170C3×#120C23112yescomplemented
171C3×#120C23112yescomplemented
172C3×#120C23124yescomplemented
173C3×#120C23124yescomplemented
174C3×#120C23112yescomplemented
175C3×#120C23112yescomplemented
176C3×#120C23112yescomplemented
177C3×#120C23124yescomplemented
178C3×C4×Q8C2312yescomplemented
179C3×C4×Q8C23112yescomplemented
180C3×C4×Q8C2316yescomplemented
181C3×C4×D4C2316yes—
182C3×C4×D4C2316yes—
183C3×C4×D4C23112yescomplemented
184C3×C4×D4C23124yescomplemented
185C3×C4×D4C23112yescomplemented
186C3×C4×D4C23124yescomplemented
187C3×C4×D4C23112yescomplemented
188C3×C4×D4C23124yescomplemented
189C3×C4×D4C23112yescomplemented
190C3×C4×D4C23112yescomplemented
191C3×#117C2316yescomplemented
192C3×#117C2313yescomplemented
193C3×#117C2316yescomplemented
194C3×#117C2316yescomplemented
195C3×#117C23124yescomplemented
196C2×C3×C22⋊C4C23112yescomplemented
197C2×C3×C22⋊C4C23112yescomplemented
198C2×C3×C22⋊C4C23124yescomplemented
199C2×C3×C22⋊C4C23124yescomplemented
200C2×C3×C22⋊C4C23112yescomplemented
201C2×C3×C42C2316yescomplemented
202C2×C3×C42C2313yescomplemented
203C2×2−1+4C22×C311yescharacteristic, complemented
204C2×H(5,𝔽2)C22×C313yescomplemented
205C23×D4C22×C312yescomplemented
206#563C22×C313yescomplemented
207#562C22×C316yescomplemented
208#562C22×C3112yescomplemented
209H(3,𝔽4)C22×C311yescharacteristic, complemented
210H(3,𝔽4)C22×C3112yescomplemented
211H(3,𝔽4)C22×C316yescomplemented
212H(3,𝔽4)C22×C3112yescomplemented
213H(3,𝔽4)C22×C316yescomplemented
214#560C22×C316yescomplemented
215#560C22×C3112yescomplemented
216#559C22×C316yescomplemented
217#559C22×C3112yescomplemented
218#556C22×C316yescomplemented
219#555C22×C3112yescomplemented
220#555C22×C316yescomplemented
221#551C22×C3112yescomplemented
222#551C22×C3124yescomplemented
223D4×Q8C22×C312yescomplemented
224#548C22×C3112yescomplemented
225#548C22×C3112yescomplemented
226#546C22×C3112yescomplemented
227#546C22×C3112yescomplemented
228#546C22×C3124yescomplemented
229#546C22×C3112yescomplemented
230#546C22×C3124yescomplemented
231#546C22×C3124yescomplemented
232D42C22×C316yescomplemented
233D42C22×C3124yescomplemented
234D42C22×C316yescomplemented
235D42C22×C3112yescomplemented
236#542C22×C3112yescomplemented
237#542C22×C3124yescomplemented
238#538C22×C3124yescomplemented
239#538C22×C3124yescomplemented
240#538C22×C3124yescomplemented
241#538C22×C3112yescomplemented
242#536C22×C313yescomplemented
243#536C22×C316yescomplemented
244#535C22×C316yescomplemented
245#535C22×C316yescomplemented
246#535C22×C316yescomplemented
247#535C22×C3124yescomplemented
248#535C22×C313yescomplemented
249#534C22×C3112yescomplemented
250#534C22×C3112yescomplemented
251#534C22×C3112yescomplemented
252#532C22×C313yescomplemented
253#532C22×C316yescomplemented
254#532C22×C316yescomplemented
255#529C22×C316yescomplemented
256#529C22×C3112yescomplemented
257C2×#124C22×C316yescomplemented
258C2×#124C22×C3112yescomplemented
259C2×#124C22×C313yescomplemented
260#525C22×C316yescomplemented
261#525C22×C316yescomplemented
262C2×#120C22×C3112yescomplemented
263C2×#120C22×C3112yescomplemented
264#518C22×C316yescomplemented
265C4×#41C22×C313yescomplemented
266C24×C3—48no—
267C24×C3—88no—
268C24×C3C24112yes—
269C24×C3C2412yes—
270C24×C3C24112yes—
271C24×C3C2416yes—
272C3×#41—212no—
273C3×#41—46no—
274C3×#41—42no—
275C3×#41—412no—
276C3×#41—412no—
277C3×#41—412no—
278C3×#41—812no—
279C2×C3×Q8—44no—
280C2×C3×Q8—46no—
281C2×C3×Q8—84no—
282C2×C3×Q8C2413yes—
283C2×C3×Q8C2412yes—
284C2×C3×Q8C24112yes—
285C2×C3×Q8C2416yes—
286C2×C3×Q8C2413yes—
287C2×C3×Q8C2411yescharacteristic
288C2×C3×D4—224no—
289C2×C3×D4—412no—
290C2×C3×D4—46no—
291C2×C3×D4—412no—
292C2×C3×D4—424no—
293C2×C3×D4—424no—
294C2×C3×D4—812no—
295C2×C3×D4—824no—
296C2×C3×D4C24112yes—
297C2×C3×D4C2416yes—
298C2×C3×D4C2416yes—
299C2×C3×D4C2416yes—
300C2×C3×D4C24124yes—
301C2×C3×D4C24112yes—
302C2×C3×D4C24112yes—
303C2×C3×D4C24124yes—
304C2×C3×D4C24112yes—
305C2×C3×D4C2413yes—
306C2×C3×D4C24112yes—
307C2×C3×D4C2416yes—
308C2×C3×D4C2413yes—
309C2×C3×D4C2416yes—
310C2×C3×D4C24112yes—
311C2×C3×D4C2411yescharacteristic
312C22×C3×C4—44no—
313C22×C3×C4C2416yes—
314C22×C3×C4C2413yes—
315C22×C3×C4C2416yes—
316C22×C3×C4C24112yes—
317C22×C3×C4C2416yes—
318C22×C3×C4C24124yes—
319C22×C3×C4C2416yes—
320C22×C3×C4C24112yes—
321C22×C3×C4C2416yes—
322C3×C4⋊C4C2416yes—
323C3×C4⋊C4C24112yes—
324C3×C4⋊C4C24112yes—
325C3×C4⋊C4C24112yes—
326C3×C4⋊C4C24112yes—
327C3×C4⋊C4C2416yes—
328C3×C4⋊C4C24124yes—
329C3×C4⋊C4C2416yes—
330C3×C22⋊C4C24112yes—
331C3×C22⋊C4C24112yes—
332C3×C22⋊C4C2416yes—
333C3×C22⋊C4C2416yes—
334C3×C22⋊C4C24112yes—
335C3×C22⋊C4C24124yes—
336C3×C22⋊C4C24112yes—
337C3×C22⋊C4C24124yes—
338C3×C22⋊C4C24124yes—
339C3×C22⋊C4C24124yes—
340C3×C22⋊C4C24124yes—
341C3×C22⋊C4C24124yes—
342C3×C22⋊C4C2416yes—
343C3×C22⋊C4C24112yes—
344C3×C42C2413yes—
345C3×C42C2416yes—
346C3×C42C2416yes—
347C3×C42C2413yes—
348C3×C42C24112yes—
349C3×C42C24112yes—
350C25C23×C314yescomplemented
3512−1+4—44no—
352H(5,𝔽2)—412no—
353C2×#41C23×C313yes—
354C2×#41C23×C313yes—
355C2×#41C23×C316yes—
356C2×#41C23×C316yes—
357C2×#41C23×C311yescharacteristic, complemented
358C2×#41C23×C316yescomplemented
359C2×#41C23×C3112yescomplemented
360C22×Q8C23×C312yescomplemented
361C22×Q8C23×C313yescomplemented
362C22×Q8C23×C314yescomplemented
363C22×D4—48no—
364C22×D4C23×C316yes—
365C22×D4C23×C316yes—
366C22×D4C23×C3112yes—
367C22×D4C23×C313yes—
368C22×D4C23×C3112yes—
369C22×D4C23×C3112yescomplemented
370C22×D4C23×C316yescomplemented
371C22×D4C23×C3124yescomplemented
372C23×C4C23×C312yescomplemented
373C4⋊Q8C23×C316yescomplemented
374C4⋊Q8C23×C313yescomplemented
375C4⋊Q8C23×C316yescomplemented
376#127C23×C316yes—
377#127C23×C313yes—
378#127C23×C3112yes—
379#127C23×C316yescomplemented
380#126C23×C3124yescomplemented
381#126C23×C3112yescomplemented
382#126C23×C3124yescomplemented
383#125C23×C316yescomplemented
384#124C23×C316yes—
385#124C23×C313yes—
386#124C23×C316yes—
387#124C23×C3112yes—
388#124C23×C316yescomplemented
389#124C23×C3112yescomplemented
390#124C23×C316yescomplemented
391#124C23×C316yescomplemented
392#124C23×C3112yescomplemented
393#124C23×C3124yescomplemented
394#124C23×C3112yescomplemented
395#124C23×C3124yescomplemented
396#124C23×C3124yescomplemented
397#124C23×C313yescomplemented
398#124C23×C3124yescomplemented
399#124C23×C3112yescomplemented
400#123C23×C316yes—
401#123C23×C3112yescomplemented
402#123C23×C316yescomplemented
403#123C23×C3124yescomplemented
404#123C23×C3112yescomplemented
405#123C23×C3124yescomplemented
406#123C23×C3124yescomplemented
407#123C23×C3124yescomplemented
408#123C23×C3112yescomplemented
409C22⋊Q8C23×C3112yescomplemented
410C22⋊Q8C23×C3112yescomplemented
411C22⋊Q8C23×C3112yescomplemented
412C22⋊Q8C23×C316yescomplemented
413C22⋊Q8C23×C3124yescomplemented
414C22⋊Q8C23×C3124yescomplemented
415#121C23×C3112yes—
416#121C23×C3112yes—
417#121C23×C3112yes—
418#121C23×C316yes—
419#121C23×C3124yes—
420#121C23×C3112yescomplemented
421#121C23×C3124yescomplemented
422#121C23×C3112yescomplemented
423#121C23×C3112yescomplemented
424#121C23×C3124yescomplemented
425#121C23×C3124yescomplemented
426#121C23×C3124yescomplemented
427#121C23×C3124yescomplemented
428#120C23×C316yes—
429#120C23×C3112yes—
430#120C23×C3124yes—
431#120C23×C3124yes—
432#120C23×C316yescomplemented
433#120C23×C3112yescomplemented
434#120C23×C3112yescomplemented
435#120C23×C3112yescomplemented
436#120C23×C3112yescomplemented
437#120C23×C3124yescomplemented
438#120C23×C3124yescomplemented
439#120C23×C3124yescomplemented
440#120C23×C3112yescomplemented
441C4×Q8C23×C316yescomplemented
442C4×Q8C23×C312yescomplemented
443C4×Q8C23×C3112yescomplemented
444C4×D4C23×C316yes—
445C4×D4C23×C316yes—
446C4×D4C23×C3112yescomplemented
447C4×D4C23×C3124yescomplemented
448C4×D4C23×C3112yescomplemented
449C4×D4C23×C3112yescomplemented
450C4×D4C23×C3124yescomplemented
451C4×D4C23×C3112yescomplemented
452C4×D4C23×C3112yescomplemented
453C4×D4C23×C3124yescomplemented
454#117C23×C316yescomplemented
455#117C23×C313yescomplemented
456#117C23×C316yescomplemented
457#117C23×C316yescomplemented
458#117C23×C3124yescomplemented
459C2×C22⋊C4C23×C3112yescomplemented
460C2×C22⋊C4C23×C3112yescomplemented
461C2×C22⋊C4C23×C3124yescomplemented
462C2×C22⋊C4C23×C3124yescomplemented
463C2×C22⋊C4C23×C3112yescomplemented
464C2×C42C23×C316yescomplemented
465C2×C42C23×C313yescomplemented
466C23×C3—224no—
467C23×C3—42no—
468C23×C3—44no—
469C23×C3—412no—
470C23×C3—424no—
471C23×C3—424no—
472C23×C3—46no—
473C23×C3—412no—
474C23×C3—832no—
475C23×C3C2516yes—
476C23×C3C25112yes—
477C23×C3C2513yes—
478C23×C3C2512yes—
479C3×Q8—26no—
480C3×Q8—41no—
481C3×Q8—46no—
482C3×Q8—42no—
483C3×Q8—412no—
484C3×Q8—43no—
485C3×D4—224no—
486C3×D4—212no—
487C3×D4—212no—
488C3×D4—412no—
489C3×D4—43no—
490C3×D4—46no—
491C3×D4—46no—
492C3×D4—412no—
493C3×D4—412no—
494C3×D4—412no—
495C3×D4—424no—
496C3×D4—46no—
497C3×D4—424no—
498C3×D4—412no—
499C3×D4—43no—
500C3×D4H(5,𝔽2)14yes—
501C2×C3×C4—212no—
502C2×C3×C4—212no—
503C2×C3×C4—26no—
504C2×C3×C4—46no—
505C2×C3×C4—412no—
506C2×C3×C4—412no—
507C2×C3×C4—424no—
508C2×C3×C4—46no—
509C2×C3×C4—46no—
510C2×C3×C4C2516yes—
511C2×C3×C4C25112yes—
512C2×C3×C4C2513yes—
513C2×C3×C4C2516yes—
514C2×C3×C4C2516yes—
515C2×C3×C4C2516yes—
516C2×C3×C4C2511yescharacteristic
517C24—48no—
518C24—88no—
519C24C24×C3112yes—
520C24C24×C3112yes—
521C24C24×C316yes—
522C24C24×C312yes—
523#41—212no—
524#41—46no—
525#41—42no—
526#41—412no—
527#41—412no—
528#41—412no—
529#41—812no—
530C2×Q8—44no—
531C2×Q8—46no—
532C2×Q8—84no—
533C2×Q8C24×C313yes—
534C2×Q8C24×C312yes—
535C2×Q8C24×C3112yes—
536C2×Q8C24×C316yes—
537C2×Q8C24×C313yes—
538C2×Q8C24×C311yescharacteristic
539C2×D4—224no—
540C2×D4—412no—
541C2×D4—46no—
542C2×D4—412no—
543C2×D4—424no—
544C2×D4—424no—
545C2×D4—812no—
546C2×D4—824no—
547C2×D4C24×C3112yes—
548C2×D4C24×C316yes—
549C2×D4C24×C316yes—
550C2×D4C24×C316yes—
551C2×D4C24×C3124yes—
552C2×D4C24×C3112yes—
553C2×D4C24×C3112yes—
554C2×D4C24×C3124yes—
555C2×D4C24×C3112yes—
556C2×D4C24×C313yes—
557C2×D4C24×C3112yes—
558C2×D4C24×C316yes—
559C2×D4C24×C313yes—
560C2×D4C24×C316yes—
561C2×D4C24×C3112yes—
562C2×D4C24×C311yescharacteristic
563C22×C4—44no—
564C22×C4C24×C316yes—
565C22×C4C24×C313yes—
566C22×C4C24×C316yes—
567C22×C4C24×C3112yes—
568C22×C4C24×C316yes—
569C22×C4C24×C3124yes—
570C22×C4C24×C316yes—
571C22×C4C24×C3112yes—
572C22×C4C24×C316yes—
573C4⋊C4C24×C316yes—
574C4⋊C4C24×C3112yes—
575C4⋊C4C24×C3112yes—
576C4⋊C4C24×C3112yes—
577C4⋊C4C24×C3112yes—
578C4⋊C4C24×C316yes—
579C4⋊C4C24×C3124yes—
580C4⋊C4C24×C316yes—
581C22⋊C4C24×C3112yes—
582C22⋊C4C24×C3112yes—
583C22⋊C4C24×C316yes—
584C22⋊C4C24×C316yes—
585C22⋊C4C24×C3112yes—
586C22⋊C4C24×C3124yes—
587C22⋊C4C24×C3112yes—
588C22⋊C4C24×C3124yes—
589C22⋊C4C24×C3124yes—
590C22⋊C4C24×C3124yes—
591C22⋊C4C24×C3124yes—
592C22⋊C4C24×C3124yes—
593C22⋊C4C24×C316yes—
594C22⋊C4C24×C3112yes—
595C42C24×C313yes—
596C42C24×C316yes—
597C42C24×C316yes—
598C42C24×C313yes—
599C42C24×C3112yes—
600C42C24×C3112yes—
601C22×C3—24no—
602C22×C3—23no—
603C22×C3—26no—
604C22×C3—212no—
605C22×C3—26no—
606C22×C3—224no—
607C22×C3—212no—
608C22×C3—48no—
609C22×C3—824no—
610C22×C3—824no—
611C22×C3—166no—
612C22×C3C2×H(5,𝔽2)14yes—
613C22×C3C2611yescharacteristic
614C3×C4—23no—
615C3×C4—26no—
616C3×C4—26no—
617C3×C4—26no—
618C3×C4—212no—
619C3×C4—26no—
620C3×C4C2×H(5,𝔽2)12yes—
621C23—224no—
622C23—42no—
623C23—44no—
624C23—412no—
625C23—424no—
626C23—424no—
627C23—46no—
628C23—412no—
629C23—832no—
630C23C25×C316yes—
631C23C25×C3112yes—
632C23C25×C313yes—
633C23C25×C312yes—
634Q8—26no—
635Q8—41no—
636Q8—46no—
637Q8—42no—
638Q8—412no—
639Q8—43no—
640D4—224no—
641D4—212no—
642D4—212no—
643D4—412no—
644D4—43no—
645D4—46no—
646D4—46no—
647D4—412no—
648D4—412no—
649D4—412no—
650D4—424no—
651D4—46no—
652D4—424no—
653D4—412no—
654D4—43no—
655D4C3×H(5,𝔽2)14yes—
656C2×C4—212no—
657C2×C4—212no—
658C2×C4—26no—
659C2×C4—46no—
660C2×C4—412no—
661C2×C4—412no—
662C2×C4—424no—
663C2×C4—46no—
664C2×C4—46no—
665C2×C4C25×C316yes—
666C2×C4C25×C3112yes—
667C2×C4C25×C313yes—
668C2×C4C25×C316yes—
669C2×C4C25×C316yes—
670C2×C4C25×C316yes—
671C2×C4C25×C311yescharacteristic
672C2×C3—24no—
673C2×C3—46no—
674C2×C3—412no—
675C2×C3—43no—
676C2×C3C22×H(5,𝔽2)11yescharacteristic
677C2×C3H(7,𝔽2)12yes—
678C22—24no—
679C22—23no—
680C22—26no—
681C22—212no—
682C22—26no—
683C22—224no—
684C22—212no—
685C22—48no—
686C22—824no—
687C22—824no—
688C22—166no—
689C22C2×C3×H(5,𝔽2)14yes—
690C22C26×C311yescharacteristic
691C4—23no—
692C4—26no—
693C4—26no—
694C4—26no—
695C4—212no—
696C4—26no—
697C4C2×C3×H(5,𝔽2)12yes—
698C3#6304511yescharacteristic, direct product factor, Sylow
699C2—24no—
700C2—46no—
701C2—412no—
702C2—43no—
703C2C22×C3×H(5,𝔽2)11yescharacteristic
704C2C3×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C3C26
commutator, Frattini, cosocleC22C26×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3558C2semidirect
2. C3×#3558C2semidirect
3. C3×#3549C2semidirect
4. C3×#3545C2semidirect
5. C3×#3540C2semidirect
6. C3×#3532C2semidirect
7. C3×#3529C2semidirect
8. C2×C3×H(3,𝔽4)C2semidirect
9. C3×#3514C2semidirect
10. C3×#3500C2semidirect
11. C3×#3484C2semidirect
12. #63045C3direct (N × H)
13. C2×C3×2−1+4C22semidirect
14. C2×C3×H(5,𝔽2)C22semidirect
15. C23×C3×D4C22semidirect
16. C3×#563C22semidirect
17. C3×#562C22semidirect
18. C3×#562C22semidirect
19. C3×H(3,𝔽4)C22semidirect
20. C3×H(3,𝔽4)C22semidirect
21. C3×H(3,𝔽4)C22semidirect
22. C3×H(3,𝔽4)C22semidirect
23. C3×H(3,𝔽4)C22semidirect
24. C3×#560C22semidirect
25. C3×#560C22semidirect
26. C3×#559C22semidirect
27. C3×#559C22semidirect
28. C3×#556C22semidirect
29. C3×#555C22semidirect
30. C3×#555C22semidirect
31. C3×#551C22semidirect
32. C3×#551C22semidirect
33. C3×D4×Q8C22semidirect
34. C3×#548C22semidirect
35. C3×#548C22semidirect
36. C3×#546C22semidirect
37. C3×#546C22semidirect
38. C3×#546C22semidirect
39. C3×#546C22semidirect
40. C3×#546C22semidirect
41. C3×#546C22semidirect
42. C3×D42C22semidirect
43. C3×D42C22semidirect
44. C3×D42C22semidirect
45. C3×D42C22semidirect
46. C3×#542C22semidirect
47. C3×#542C22semidirect
48. C3×#538C22semidirect
49. C3×#538C22semidirect
50. C3×#538C22semidirect
51. C3×#538C22semidirect
52. C3×#536C22semidirect
53. C3×#536C22semidirect
54. C3×#535C22semidirect
55. C3×#535C22semidirect
56. C3×#535C22semidirect
57. C3×#535C22semidirect
58. C3×#535C22semidirect
59. C3×#534C22semidirect
60. C3×#534C22semidirect
61. C3×#534C22semidirect
62. C3×#532C22semidirect
63. C3×#532C22semidirect
64. C3×#532C22semidirect
65. C3×#529C22semidirect
66. C3×#529C22semidirect
67. C2×C3×#124C22semidirect
68. C2×C3×#124C22semidirect
69. C2×C3×#124C22semidirect
70. C3×#525C22semidirect
71. C3×#525C22semidirect
72. C2×C3×#120C22semidirect
73. C2×C3×#120C22semidirect
74. C3×#518C22semidirect
75. C3×C4×#41C22semidirect
76. #3558C2×C3semidirect
77. #3558C2×C3semidirect
78. #3549C2×C3semidirect
79. #3545C2×C3semidirect
80. #3540C2×C3semidirect
81. #3532C2×C3semidirect
82. #3529C2×C3semidirect
83. C2×H(3,𝔽4)C2×C3semidirect
84. #3514C2×C3semidirect
85. #3500C2×C3semidirect
86. #3484C2×C3semidirect
87. C25×C3C23semidirect
94. C2×C3×#41C23semidirect
95. C2×C3×#41C23semidirect
96. C2×C3×#41C23semidirect
97. C22×C3×Q8C23semidirect
98. C22×C3×Q8C23semidirect
99. C22×C3×Q8C23semidirect
106. C22×C3×D4C23semidirect
107. C22×C3×D4C23semidirect
108. C22×C3×D4C23semidirect
109. C23×C3×C4C23semidirect
110. C3×C4⋊Q8C23semidirect
111. C3×C4⋊Q8C23semidirect
112. C3×C4⋊Q8C23semidirect
116. C3×#127C23semidirect
117. C3×#126C23semidirect
118. C3×#126C23semidirect
119. C3×#126C23semidirect
120. C3×#125C23semidirect
125. C3×#124C23semidirect
126. C3×#124C23semidirect
127. C3×#124C23semidirect
128. C3×#124C23semidirect
129. C3×#124C23semidirect
130. C3×#124C23semidirect
131. C3×#124C23semidirect
132. C3×#124C23semidirect
133. C3×#124C23semidirect
134. C3×#124C23semidirect
135. C3×#124C23semidirect
136. C3×#124C23semidirect
138. C3×#123C23semidirect
139. C3×#123C23semidirect
140. C3×#123C23semidirect
141. C3×#123C23semidirect
142. C3×#123C23semidirect
143. C3×#123C23semidirect
144. C3×#123C23semidirect
145. C3×#123C23semidirect
146. C3×C22⋊Q8C23semidirect
147. C3×C22⋊Q8C23semidirect
148. C3×C22⋊Q8C23semidirect
149. C3×C22⋊Q8C23semidirect
150. C3×C22⋊Q8C23semidirect
151. C3×C22⋊Q8C23semidirect
157. C3×#121C23semidirect
158. C3×#121C23semidirect
159. C3×#121C23semidirect
160. C3×#121C23semidirect
161. C3×#121C23semidirect
162. C3×#121C23semidirect
163. C3×#121C23semidirect
164. C3×#121C23semidirect
169. C3×#120C23semidirect
170. C3×#120C23semidirect
171. C3×#120C23semidirect
172. C3×#120C23semidirect
173. C3×#120C23semidirect
174. C3×#120C23semidirect
175. C3×#120C23semidirect
176. C3×#120C23semidirect
177. C3×#120C23semidirect
178. C3×C4×Q8C23semidirect
179. C3×C4×Q8C23semidirect
180. C3×C4×Q8C23semidirect
183. C3×C4×D4C23semidirect
184. C3×C4×D4C23semidirect
185. C3×C4×D4C23semidirect
186. C3×C4×D4C23semidirect
187. C3×C4×D4C23semidirect
188. C3×C4×D4C23semidirect
189. C3×C4×D4C23semidirect
190. C3×C4×D4C23semidirect
191. C3×#117C23semidirect
192. C3×#117C23semidirect
193. C3×#117C23semidirect
194. C3×#117C23semidirect
195. C3×#117C23semidirect
196. C2×C3×C22⋊C4C23semidirect
197. C2×C3×C22⋊C4C23semidirect
198. C2×C3×C22⋊C4C23semidirect
199. C2×C3×C22⋊C4C23semidirect
200. C2×C3×C22⋊C4C23semidirect
201. C2×C3×C42C23semidirect
202. C2×C3×C42C23semidirect
203. C2×2−1+4C22×C3semidirect
204. C2×H(5,𝔽2)C22×C3semidirect
205. C23×D4C22×C3semidirect
206. #563C22×C3semidirect
207. #562C22×C3semidirect
208. #562C22×C3semidirect
209. H(3,𝔽4)C22×C3semidirect
210. H(3,𝔽4)C22×C3semidirect
211. H(3,𝔽4)C22×C3semidirect
212. H(3,𝔽4)C22×C3semidirect
213. H(3,𝔽4)C22×C3semidirect
214. #560C22×C3semidirect
215. #560C22×C3semidirect
216. #559C22×C3semidirect
217. #559C22×C3semidirect
218. #556C22×C3semidirect
219. #555C22×C3semidirect
220. #555C22×C3semidirect
221. #551C22×C3semidirect
222. #551C22×C3semidirect
223. D4×Q8C22×C3semidirect
224. #548C22×C3semidirect
225. #548C22×C3semidirect
226. #546C22×C3semidirect
227. #546C22×C3semidirect
228. #546C22×C3semidirect
229. #546C22×C3semidirect
230. #546C22×C3semidirect
231. #546C22×C3semidirect
232. D42C22×C3semidirect
233. D42C22×C3semidirect
234. D42C22×C3semidirect
235. D42C22×C3semidirect
236. #542C22×C3semidirect
237. #542C22×C3semidirect
238. #538C22×C3semidirect
239. #538C22×C3semidirect
240. #538C22×C3semidirect
241. #538C22×C3semidirect
242. #536C22×C3semidirect
243. #536C22×C3semidirect
244. #535C22×C3semidirect
245. #535C22×C3semidirect
246. #535C22×C3semidirect
247. #535C22×C3semidirect
248. #535C22×C3semidirect
249. #534C22×C3semidirect
250. #534C22×C3semidirect
251. #534C22×C3semidirect
252. #532C22×C3semidirect
253. #532C22×C3semidirect
254. #532C22×C3semidirect
255. #529C22×C3semidirect
256. #529C22×C3semidirect
257. C2×#124C22×C3semidirect
258. C2×#124C22×C3semidirect
259. C2×#124C22×C3semidirect
260. #525C22×C3semidirect
261. #525C22×C3semidirect
262. C2×#120C22×C3semidirect
263. C2×#120C22×C3semidirect
264. #518C22×C3semidirect
265. C4×#41C22×C3semidirect
350. C25C23×C3semidirect
357. C2×#41C23×C3semidirect
358. C2×#41C23×C3semidirect
359. C2×#41C23×C3semidirect
360. C22×Q8C23×C3semidirect
361. C22×Q8C23×C3semidirect
362. C22×Q8C23×C3semidirect
369. C22×D4C23×C3semidirect
370. C22×D4C23×C3semidirect
371. C22×D4C23×C3semidirect
372. C23×C4C23×C3semidirect
373. C4⋊Q8C23×C3semidirect
374. C4⋊Q8C23×C3semidirect
375. C4⋊Q8C23×C3semidirect
379. #127C23×C3semidirect
380. #126C23×C3semidirect
381. #126C23×C3semidirect
382. #126C23×C3semidirect
383. #125C23×C3semidirect
388. #124C23×C3semidirect
389. #124C23×C3semidirect
390. #124C23×C3semidirect
391. #124C23×C3semidirect
392. #124C23×C3semidirect
393. #124C23×C3semidirect
394. #124C23×C3semidirect
395. #124C23×C3semidirect
396. #124C23×C3semidirect
397. #124C23×C3semidirect
398. #124C23×C3semidirect
399. #124C23×C3semidirect
401. #123C23×C3semidirect
402. #123C23×C3semidirect
403. #123C23×C3semidirect
404. #123C23×C3semidirect
405. #123C23×C3semidirect
406. #123C23×C3semidirect
407. #123C23×C3semidirect
408. #123C23×C3semidirect
409. C22⋊Q8C23×C3semidirect
410. C22⋊Q8C23×C3semidirect
411. C22⋊Q8C23×C3semidirect
412. C22⋊Q8C23×C3semidirect
413. C22⋊Q8C23×C3semidirect
414. C22⋊Q8C23×C3semidirect
420. #121C23×C3semidirect
421. #121C23×C3semidirect
422. #121C23×C3semidirect
423. #121C23×C3semidirect
424. #121C23×C3semidirect
425. #121C23×C3semidirect
426. #121C23×C3semidirect
427. #121C23×C3semidirect
432. #120C23×C3semidirect
433. #120C23×C3semidirect
434. #120C23×C3semidirect
435. #120C23×C3semidirect
436. #120C23×C3semidirect
437. #120C23×C3semidirect
438. #120C23×C3semidirect
439. #120C23×C3semidirect
440. #120C23×C3semidirect
441. C4×Q8C23×C3semidirect
442. C4×Q8C23×C3semidirect
443. C4×Q8C23×C3semidirect
446. C4×D4C23×C3semidirect
447. C4×D4C23×C3semidirect
448. C4×D4C23×C3semidirect
449. C4×D4C23×C3semidirect
450. C4×D4C23×C3semidirect
451. C4×D4C23×C3semidirect
452. C4×D4C23×C3semidirect
453. C4×D4C23×C3semidirect
454. #117C23×C3semidirect
455. #117C23×C3semidirect
456. #117C23×C3semidirect
457. #117C23×C3semidirect
458. #117C23×C3semidirect
459. C2×C22⋊C4C23×C3semidirect
460. C2×C22⋊C4C23×C3semidirect
461. C2×C22⋊C4C23×C3semidirect
462. C2×C22⋊C4C23×C3semidirect
463. C2×C22⋊C4C23×C3semidirect
464. C2×C42C23×C3semidirect
465. C2×C42C23×C3semidirect
698. C3#63045direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35582
C3×#35492
C3×#35452
C3×#35402
C3×#35322
C3×#35292
C2×C3×H(3,𝔽4)2
C3×#35142
C3×#35002
C3×#34842
#630453