Finite Group Databasebeta

← C2×#10594164 #11902914

Subgroups — C2×#10594164 #11902914

Order 1152.

2993 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#878C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic
5C2×Dic3×#67C211yesmaximal, characteristic, complemented
6C22×#3722C211yesmaximal, characteristic, complemented
7C2×#63955C211yesmaximal, characteristic, complemented
8C2×#63907C211yesmaximal, characteristic, complemented
9C2×#63890C211yesmaximal, characteristic, complemented
10C2×#63881C211yesmaximal, characteristic, complemented
11C2×#63871C211yesmaximal, characteristic, complemented
12C2×#63853C211yesmaximal, characteristic, complemented
13C2×#63849C211yesmaximal, characteristic, complemented
14C2×#63848C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594164C2116yesmaximal, direct product factor
17C2×#5658—31nomaximal
18C2×#5637—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C22⋊C4×C3⋊D3C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C3×#886C2218yescomplemented
43C3×#878C2218yescomplemented
44#63981C2218yes—
45Dic3×#67C2218yescomplemented
46C2×Dic3⋊Dic3C2211yescharacteristic, complemented
47C2×Dic3⋊Dic3C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2218yescomplemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63955C2218yescomplemented
58C2×Dic32C2211yescharacteristic, complemented
59C2×Dic32C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63907C2218yescomplemented
62#63890C2218yescomplemented
63#63881C2218yescomplemented
64#63871C2218yescomplemented
65#63853C2218yescomplemented
66#63849C2218yescomplemented
67#63848C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#937—31no—
74C2×D4×Dic3—31no—
75C2×C4×#67—31no—
76C22×(C2×D3)⋊C4—31no—
77C22×(C2×D3)⋊C4—31no—
78C2×#926—31no—
79#5658—316no—
80#5637—316no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#898—31no—
84C2×#898—31no—
85C2×#897—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#893—31no—
89C2×#892—31no—
90C2×#892—31no—
91C2×#886—31no—
92C2×#886D311yescharacteristic, complemented
93C2×#885—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#67⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—61no—
100C2×#878D311yescharacteristic, complemented
101C2×#877—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—24no—
104C23×C3⋊D3—24no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2314yes—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4×C3⋊D3—24no—
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×C4×C3⋊D3C2314yes—
118C2×C3×#67—24no—
119C2×C3×#67C2314yes—
120C22×C3×Dic3—24no—
121C22×C3×Dic3—42no—
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2314yes—
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yescomplemented
133C2×#626—24no—
134C2×#626—42no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yescomplemented
139C32×C22⋊C4C2314yes—
140#3757C2314yes—
141#3752C2314yes—
142#3752C2314yes—
143C3×#217C2314yes—
144C3×(C2×D3)⋊C4C2314yescomplemented
145C3×(C2×D3)⋊C4C2314yescomplemented
146C3×C4⋊Dic3C2314yescomplemented
147C3×C4⋊Dic3C2314yescomplemented
148C3×C4⋊Dic3C2314yescomplemented
149C3×Dic3⋊C4C2314yescomplemented
150C3×Dic3⋊C4C2314yescomplemented
151Dic3⋊Dic3C2314yescomplemented
152Dic3⋊Dic3C2314yescomplemented
153Dic3⋊Dic3C2314yescomplemented
154#3722C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160(C2×D3)⋊Dic3C2314yescomplemented
161Dic32C2314yescomplemented
162Dic32C2314yescomplemented
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C24×D3—61no—
168C22×C3×Q8—31no—
169C22×C3×D4—31no—
170C23×C3×C4—31no—
171C23×C3×C4—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67C2×D311yescharacteristic
175C23×Dic3—31no—
176C23×Dic3C2×D311yescharacteristic
177C23×Dic3C2×D311yescharacteristic
178C22×D12—31no—
179C22×D12—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—61no—
186C22×C4×D3—61no—
187C22×Dic6C2×D311yescharacteristic, complemented
188C3×#123—38no—
189C3×C22⋊Q8—38no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—21no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—61no—
205C2×#217C2×D311yescharacteristic
206#947—38no—
207#946—38no—
208#937—38no—
209D4×Dic3—38no—
210C4×#67—38no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—38no—
217C2×(C2×D3)⋊C4—38no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—61no—
231C2×(C2×D3)⋊C4—61no—
232C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
233C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
234#926—38no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3C2×D311yescharacteristic, complemented
239C2×C4⋊Dic3C2×D311yescharacteristic, complemented
240C2×C4⋊Dic3C2×D311yescharacteristic, complemented
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4C2×D311yescharacteristic, complemented
245C2×Dic3⋊C4C2×D311yescharacteristic, complemented
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252#898—38no—
253#898—38no—
254#898—38no—
255#898—38no—
256#897—38no—
257#894—38no—
258#894—38no—
259#893—38no—
260#892—38no—
261#892—38no—
262#886—38no—
263#886C2×D318yescomplemented
264#885—38no—
265#883—38no—
266#882—38no—
267#67⋊C4—38no—
268D3×C22⋊C4—38no—
269D3×C22⋊C4—38no—
270D3×C22⋊C4—68no—
271#878C2×D318yescomplemented
272#877—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—28no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—28no—
285C22×C3⋊D3—44no—
286C22×C3⋊D3—416no—
287C22×C3⋊D3#4114yes—
288C22×C3⋊D3C2412yes—
289C22×C3⋊D3C2412yes—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3C2412yes—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—28no—
303C4×C3⋊D3—44no—
304C3×#67—28no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—28no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—44no—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×Dic6—44no—
322#626—28no—
323#626—44no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—31no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—31no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×#117—91no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—21no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—31no—
349C23×D3—34no—
350C23×D3—34no—
351C23×D3—61no—
352C23×D3—64no—
353C23×D3—61no—
354C23×D3—64no—
355C23×D3—64no—
356C23×D3—68no—
357C23×D3—64no—
358C23×D3—64no—
359C23×D3—124no—
360C23×D3—122no—
361C23×D3—122no—
362C23×D3—124no—
363C23×D3C22×D311yescharacteristic
364C2×C3×Q8—34no—
365C2×C3×Q8—122no—
366C2×C3×D4—34no—
367C2×C3×D4—64no—
368C22×C3×C4—21no—
369C22×C3×C4—21no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—34no—
378C22×C3×C4—34no—
379C22×C3×C4—64no—
380C22×C3×C4—122no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—24no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—64no—
389C2×#67—122no—
390C2×#67C22×D314yes—
391C22×Dic3—24no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—34no—
397C22×Dic3—42no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—122no—
401C22×Dic3C22×D314yes—
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D314yes—
410C2×D12—34no—
411C2×D12—34no—
412C2×D12—64no—
413C2×D12—122no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—64no—
423C2×C4×D3—124no—
424C2×C4×D3—122no—
425C2×C4×D3—122no—
426C2×C4×D3—122no—
427C2×C4×D3—124no—
428C2×Dic6—42no—
429C2×Dic6C22×D314yescomplemented
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C22⋊C4—24no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4C22×D314yes—
440C3×C22⋊C4C22×D314yes—
441#217—34no—
442#217—34no—
443#217—34no—
444#217—64no—
445#217C22×D314yes—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—64no—
464(C2×D3)⋊C4—64no—
465(C2×D3)⋊C4C22×D314yescomplemented
466(C2×D3)⋊C4C22×D314yescomplemented
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3C22×D314yescomplemented
471C4⋊Dic3C22×D314yescomplemented
472C4⋊Dic3C22×D314yescomplemented
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4C22×D314yescomplemented
477Dic3⋊C4C22×D314yescomplemented
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—34no—
484C22×C32—28no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32C2×#4114yes—
488C22×C32C2×#4112yes—
489C22×C32C2×#4112yes—
490C22×C32H(5,𝔽2)12yes—
491C22×C32C2511yescharacteristic
492C2×C3⋊D3—28no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—416no—
499C2×C3⋊D3—44no—
500C2×C3⋊D3C2×#4114yes—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—44no—
505C32×C4—22no—
506C32×C4—22no—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C25—91no—
517C22×Q8—31no—
518C22×D4—31no—
519C22×D4—91no—
520C22×D4—91no—
521C23×C4—31no—
522C23×C4—31no—
523C23×C4—91no—
524C23×C4—91no—
525C23×C4—91no—
526#126—98no—
527#126—98no—
528#124—98no—
529#123—38no—
530#123—98no—
531#123—98no—
532C22⋊Q8—38no—
533C22⋊Q8—98no—
534#120—98no—
535C4×D4—98no—
536C4×D4—98no—
537#117—98no—
538#117—98no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—31no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—98no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—98no—
562C2×C22⋊C4D3211yescharacteristic
563C2×C42—91no—
564C2×C42—91no—
565C2×C42—91no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—21no—
572C23×C3—24no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3#23714yes—
580C23×C3#23914yes—
581C23×C3C23×D312yes—
582C23×C3C23×D312yes—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—34no—
589C22×D3—34no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—64no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—68no—
598C22×D3—68no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—616no—
606C22×D3—64no—
607C22×D3—68no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—68no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—128no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—124no—
619C22×D3—124no—
620C22×D3—1216no—
621C22×D3—1216no—
622C22×D3—128no—
623C22×D3—1232no—
624C22×D3C23×D312yes—
625C3×Q8—124no—
626C3×D4—68no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—22no—
631C2×C3×C4—22no—
632C2×C3×C4—22no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—42no—
641C2×C3×C4—42no—
642C2×C3×C4—68no—
643C2×C3×C4—62no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—62no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—62no—
650C2×C3×C4—124no—
651C2×C3×C4C23×D312yes—
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D312yes—
655#67—28no—
656#67—68no—
657#67—124no—
658C2×Dic3—28no—
659C2×Dic3—22no—
660C2×Dic3—22no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—32no—
669C2×Dic3—32no—
670C2×Dic3—44no—
671C2×Dic3—62no—
672C2×Dic3—62no—
673C2×Dic3—62no—
674C2×Dic3—62no—
675C2×Dic3—62no—
676C2×Dic3—62no—
677C2×Dic3—122no—
678C2×Dic3—122no—
679C2×Dic3—124no—
680C2×Dic3C23×D312yes—
681C2×Dic3C23×D312yes—
682C2×Dic3C23×D312yes—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D312yes—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D312yes—
687D12—68no—
688D12—124no—
689C4×D3—68no—
690C4×D3—68no—
691C4×D3—128no—
692C4×D3—124no—
693C4×D3—124no—
694C4×D3—124no—
695C4×D3—128no—
696Dic6—44no—
697C2×C32—24no—
698C2×C32#55114yescomplemented
699C2×C32C22×#4111yescharacteristic
700C2×C32C22×#4111yescharacteristic
701C2×C32C2×H(5,𝔽2)11yescharacteristic
702C3⋊D3—24no—
703C3⋊D3—42no—
704C3×D3—42no—
705C24—31no—
706C24—91no—
707C24—91no—
708C24—94no—
709C24—184no—
710C24—184no—
711C24—362no—
712C24C2×D3211yescharacteristic
713C2×Q8—34no—
714C2×Q8—122no—
715C2×D4—34no—
716C2×D4—64no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—184no—
720C2×D4—362no—
721C22×C4—34no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—34no—
730C22×C4—64no—
731C22×C4—94no—
732C22×C4—91no—
733C22×C4—91no—
734C22×C4—94no—
735C22×C4—94no—
736C22×C4—122no—
737C22×C4—184no—
738C22×C4—362no—
739C22×C4—362no—
740C22×C4C2×D3211yescharacteristic
741C22×C4C2×D3211yescharacteristic
742C4⋊C4—34no—
743C4⋊C4—34no—
744C4⋊C4—34no—
745C4⋊C4—34no—
746C4⋊C4—34no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C22⋊C4—34no—
751C22⋊C4—34no—
752C22⋊C4—34no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C22⋊C4—94no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—94no—
762C22⋊C4—94no—
763C22⋊C4C2×D3214yes—
764C42—94no—
765C42—94no—
766C42—94no—
767C22×C3—28no—
768C22×C3—28no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—21no—
778C22×C3—42no—
779C22×C3—42no—
780C22×C3—48no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—124no—
785C22×C3C2×#23714yes—
786C22×C3C2×#23712yes—
787C22×C3#100412yes—
788C22×C3C2×#23914yes—
789C22×C3C2×#23912yes—
790C22×C3D3×#4112yes—
791C22×C3D3×#4112yes—
792C22×C3#100912yes—
793C22×C3C24×D311yescharacteristic
794C22×C3C24×D311yescharacteristic
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—34no—
799C2×D3—34no—
800C2×D3—44no—
801C2×D3—64no—
802C2×D3—64no—
803C2×D3—64no—
804C2×D3—616no—
805C2×D3—68no—
806C2×D3—68no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—64no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—62no—
817C2×D3—62no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—1216no—
821C2×D3—1216no—
822C2×D3—1232no—
823C2×D3—128no—
824C2×D3—124no—
825C2×D3—124no—
826C3×C4—22no—
827C3×C4—22no—
828C3×C4—22no—
829C3×C4—22no—
830C3×C4—42no—
831C3×C4—42no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—62no—
835C3×C4—62no—
836C3×C4—62no—
837C3×C4—62no—
838C3×C4—62no—
839Dic3—22no—
840Dic3—22no—
841Dic3—22no—
842Dic3—22no—
843Dic3—22no—
844Dic3—22no—
845Dic3—22no—
846Dic3—62no—
847Dic3—62no—
848Dic3—62no—
849Dic3—62no—
850Dic3—122no—
851Dic3—122no—
852C32C2×#55111yescharacteristic, complemented, Sylow
853C23—22no—
854C23—22no—
855C23—32no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—94no—
860C23—92no—
861C23—92no—
862C23—188no—
863C23—182no—
864C23—182no—
865C23—188no—
866C23—182no—
867C23—182no—
868C23—182no—
869C23—364no—
870C23—3616no—
871C23#379614yes—
872C23C22×D3212yes—
873C23C22×D3211yescharacteristic
874Q8—124no—
875D4—68no—
876D4—188no—
877D4—364no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—32no—
885C2×C4—32no—
886C2×C4—32no—
887C2×C4—68no—
888C2×C4—62no—
889C2×C4—62no—
890C2×C4—62no—
891C2×C4—62no—
892C2×C4—62no—
893C2×C4—62no—
894C2×C4—62no—
895C2×C4—92no—
896C2×C4—92no—
897C2×C4—124no—
898C2×C4—188no—
899C2×C4—182no—
900C2×C4—182no—
901C2×C4—364no—
902C2×C4—364no—
903C2×C4C22×D3212yes—
904C2×C4C22×D3212yes—
905C2×C3—24no—
906C2×C3—24no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—24no—
911C2×C3—44no—
912C2×C3—122no—
913C2×C3#563714yescomplemented
914C2×C3#565814yescomplemented
915C2×C3C22×#23711yescharacteristic
916C2×C3C2×#100411yescharacteristic
917C2×C3C22×#23911yescharacteristic
918C2×C3C2×D3×#4111yescharacteristic
919C2×C3C2×D3×#4111yescharacteristic
920C2×C3C2×#100911yescharacteristic
921D3—42no—
922D3—68no—
923D3—64no—
924D3—64no—
925D3—124no—
926D3—122no—
927D3—122no—
928C22—22no—
929C22—22no—
930C22—28no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—94no—
935C22—124no—
936C22—182no—
937C22—182no—
938C22—188no—
939C22—182no—
940C22—182no—
941C22—182no—
942C22—3616no—
943C22—364no—
944C22C2×#379614yes—
945C22C2×#379612yes—
946C22#6431212yes—
947C22#6431412yes—
948C22C23×D3211yescharacteristic
949C4—22no—
950C4—22no—
951C4—62no—
952C4—62no—
953C4—62no—
954C4—62no—
955C4—62no—
956C4—62no—
957C4—62no—
958C4—182no—
959C4—182no—
960C3—21no—
961C3C2×#563711yescharacteristic, complemented
962C3C2×#565811yescharacteristic, complemented
963C2—24no—
964C2—122no—
965C2—184no—
966C2—362no—
967C2#1059416414yesdirect product factor
968C2C22×#379611yescharacteristic
969C2C2×#6431211yescharacteristic
970C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63981C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊C4×C3⋊D3C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#878C2semidirect
5. C2×Dic3×#67C2semidirect
6. C22×#3722C2semidirect
7. C2×#63955C2semidirect
8. C2×#63907C2semidirect
9. C2×#63890C2semidirect
10. C2×#63881C2semidirect
11. C2×#63871C2semidirect
12. C2×#63853C2semidirect
13. C2×#63849C2semidirect
14. C2×#63848C2semidirect
15. C2×#63848C2semidirect
16. #10594164C2direct (N × H)
25. C22×C3×Dic6C22semidirect
28. C22×D3×Dic3C22semidirect
33. C22⋊C4×C3⋊D3C22semidirect
35. C2×C3×(C2×D3)⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×C4⋊Dic3C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C3×#886C22semidirect
43. C3×#878C22semidirect
45. Dic3×#67C22semidirect
46. C2×Dic3⋊Dic3C22semidirect
47. C2×Dic3⋊Dic3C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. #63955C22semidirect
58. C2×Dic32C22semidirect
59. C2×Dic32C22semidirect
60. C2×Dic32C22semidirect
61. #63907C22semidirect
62. #63890C22semidirect
63. #63881C22semidirect
64. #63871C22semidirect
65. #63853C22semidirect
66. #63849C22semidirect
67. #63848C22semidirect
68. #63848C22semidirect
92. C2×#886D3semidirect
100. C2×#878D3semidirect
132. C2×C3×Dic6C23semidirect
138. C2×D3×Dic3C23semidirect
144. C3×(C2×D3)⋊C4C23semidirect
145. C3×(C2×D3)⋊C4C23semidirect
146. C3×C4⋊Dic3C23semidirect
147. C3×C4⋊Dic3C23semidirect
148. C3×C4⋊Dic3C23semidirect
149. C3×Dic3⋊C4C23semidirect
150. C3×Dic3⋊C4C23semidirect
151. Dic3⋊Dic3C23semidirect
152. Dic3⋊Dic3C23semidirect
153. Dic3⋊Dic3C23semidirect
160. (C2×D3)⋊Dic3C23semidirect
161. Dic32C23semidirect
162. Dic32C23semidirect
163. Dic32C23semidirect
187. C22×Dic6C2×D3semidirect
232. C2×(C2×D3)⋊C4C2×D3semidirect
233. C2×(C2×D3)⋊C4C2×D3semidirect
238. C2×C4⋊Dic3C2×D3semidirect
239. C2×C4⋊Dic3C2×D3semidirect
240. C2×C4⋊Dic3C2×D3semidirect
244. C2×Dic3⋊C4C2×D3semidirect
245. C2×Dic3⋊C4C2×D3semidirect
263. #886C2×D3semidirect
271. #878C2×D3semidirect
429. C2×Dic6C22×D3semidirect
465. (C2×D3)⋊C4C22×D3semidirect
466. (C2×D3)⋊C4C22×D3semidirect
470. C4⋊Dic3C22×D3semidirect
471. C4⋊Dic3C22×D3semidirect
472. C4⋊Dic3C22×D3semidirect
476. Dic3⋊C4C22×D3semidirect
477. Dic3⋊C4C22×D3semidirect
698. C2×C32#551semidirect
852. C32C2×#551semidirect
913. C2×C3#5637semidirect
914. C2×C3#5658semidirect
961. C3C2×#5637semidirect
962. C3C2×#5658semidirect
967. C2#10594164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×C3×#8862
C2×C3×#8782
C2×#639812
C2×Dic3×#672
C22×#37222
C2×#639552
C2×#639072
C2×#638902
C2×#638812
C2×#638712
C2×#638532
C2×#638492
C2×#638482
#105941642
C2×#56583
C2×#56373