Finite Group Databasebeta

← C2×#10594323 #11901599

Subgroups — C2×#10594323 #11901599

Order 1152.

2169 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic
2C2×C3×#890C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×#63868C211yesmaximal, characteristic
5C2×#63868C211yesmaximal, characteristic
6C2×#63865C211yesmaximal, characteristic
7C2×#63849C211yesmaximal, characteristic
8C2×#63848C211yesmaximal, characteristic
9C2×#63848C211yesmaximal, characteristic
10C2×#63847C211yesmaximal, characteristic, complemented
11C2×#63847C211yesmaximal, characteristic, complemented
12C2×#63846C211yesmaximal, characteristic, complemented
13C2×#63844C211yesmaximal, characteristic, complemented
14C2×#63840C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594323C2116yesmaximal, direct product factor
17C2×#5696—31nomaximal
18C2×#5696—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64105C2218yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C3×#890C2218yescomplemented
41C3×#889C2218yescomplemented
42C2×#3724C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×Dic32C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63868C2218yes—
58#63868C2218yes—
59#63865C2218yes—
60#63849C2218yes—
61#63848C2218yes—
62#63848C2218yes—
63#63847C2218yescomplemented
64#63847C2218yescomplemented
65#63846C2218yescomplemented
66#63844C2218yescomplemented
67#63840C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×#125—31no—
71#5696—316no—
72#5696—316no—
73C2×#898—31no—
74C2×#898—31no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#896—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#896—61no—
84C2×#892—31no—
85C2×#892—31no—
86C2×#890—31no—
87C2×#890D311yescharacteristic, complemented
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#889—31no—
93C2×#889D311yescharacteristic, complemented
94C2×#888—31no—
95C2×#888—31no—
96C2×#887—31no—
97C2×#887—31no—
98C2×#876—31no—
99C2×#876—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C23×C3⋊D3C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4×C3⋊D3—24no—
110C2×C4×C3⋊D3C2314yes—
111C2×#634—24no—
112C2×#634C2314yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×#627—24no—
122C2×#627C2314yes—
123C32×C4⋊C4C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3750C2314yes—
127#3750C2314yes—
128C3×C4⋊Dic3C2314yes—
129C3×C4⋊Dic3C2314yes—
130C3×C4⋊Dic3C2314yes—
131C3×C4⋊Dic3C2314yes—
132C3×Dic3⋊C4C2314yes—
133C3×Dic3⋊C4C2314yes—
134C3×Dic3⋊C4C2314yes—
135C3×Dic3⋊C4C2314yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×C4×Dic3C2314yes—
139C3×C4×Dic3C2314yes—
140#3724C2314yes—
141#3724C2314yes—
142#3724C2314yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147#3722C2314yes—
148#3722C2314yes—
149#3722C2314yes—
150#3722C2314yes—
151Dic32C2314yes—
152Dic32C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155C2×#541—91noSylow
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×Dic6—31no—
160C22×Dic6—31no—
161C22×Dic6—31no—
162C22×Dic6—31no—
163C22×Dic6—61no—
164C3×#125—38no—
165C3×#125—38no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4C2×D311yescharacteristic
178C2×C3×C4⋊C4C2×D311yescharacteristic
179C2×C3×C42—31no—
180C2×C3×C42—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—61no—
194C2×(C2×D3)⋊C4—61no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3C2×D311yescharacteristic
200C2×C4⋊Dic3C2×D311yescharacteristic
201C2×C4⋊Dic3C2×D311yescharacteristic
202C2×C4⋊Dic3C2×D311yescharacteristic
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—61no—
218C2×Dic3⋊C4—61no—
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×Dic3⋊C4C2×D311yescharacteristic
222C2×Dic3⋊C4C2×D311yescharacteristic
223C2×Dic3⋊C4C2×D311yescharacteristic
224C2×Dic3⋊C4C2×D311yescharacteristic
225C2×C4×Dic3—31no—
226C2×C4×Dic3—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3C2×D311yescharacteristic
234C2×C4×Dic3C2×D311yescharacteristic
235#898—38no—
236#898—38no—
237#898—38no—
238#898—38no—
239#898—38no—
240#898—38no—
241#896—38no—
242#896—38no—
243#896—38no—
244#896—38no—
245#896—68no—
246#892—38no—
247#892—38no—
248#890—38no—
249#890C2×D318yescomplemented
250#889—38no—
251#889—38no—
252#889—38no—
253#889—38no—
254#889—38no—
255#889C2×D318yescomplemented
256#888—38no—
257#888—38no—
258#887—38no—
259#887—38no—
260#876—38no—
261#876—38no—
262C4×Dic6—38no—
263C4×Dic6—38no—
264C23×C32C2411yescharacteristic
265C22×C3⋊D3—22no—
266C22×C3⋊D3—22no—
267C22×C3⋊D3—22no—
268C22×C3⋊D3C2412yes—
269C2×C32×C4—22no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4C2412yes—
273C2×C32×C4C2412yes—
274C2×C32×C4C2412yes—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3—22no—
277C2×C3⋊Dic3#4114yes—
278C2×C3⋊Dic3C2412yes—
279C2×C3⋊Dic3C2412yes—
280C2×C3⋊Dic3C2412yes—
281C4×C3⋊D3—28no—
282#634—28no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299#627—28no—
300#541—916no—
301C2×C4⋊Q8—91no—
302C2×#126—91no—
303C2×#126—91no—
304C2×#126—91no—
305C2×#126—91no—
306C2×#125—31no—
307C2×#125—31no—
308C2×#125—91no—
309C2×#125—91no—
310C2×#125—91no—
311C2×C22⋊Q8—91no—
312C2×C22⋊Q8—91no—
313C2×C4×Q8—91no—
314C2×C4×Q8—91no—
315C2×#117—91no—
316C23×D3—31no—
317C23×D3—31no—
318C23×D3—61no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—61no—
343C22×Dic3—61no—
344C22×Dic3—61no—
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C22×Dic3C22×D311yescharacteristic
348C22×Dic3C22×D311yescharacteristic
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C2×C4×D3—34no—
354C2×C4×D3—34no—
355C2×C4×D3—64no—
356C2×C4×D3—64no—
357C2×C4×D3—64no—
358C2×C4×D3—124no—
359C2×Dic6—34no—
360C2×Dic6—34no—
361C2×Dic6—34no—
362C2×Dic6—34no—
363C2×Dic6—64no—
364C2×Dic6—64no—
365C2×Dic6—64no—
366C2×Dic6—64no—
367C2×Dic6—64no—
368C2×Dic6—124no—
369C3×C4⋊C4—24no—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—34no—
372C3×C4⋊C4—34no—
373C3×C4⋊C4—34no—
374C3×C4⋊C4—34no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—34no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4C22×D314yes—
381C3×C4⋊C4C22×D314yes—
382C3×C42—34no—
383C3×C42—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—64no—
397(C2×D3)⋊C4—64no—
398C4⋊Dic3—34no—
399C4⋊Dic3—34no—
400C4⋊Dic3—34no—
401C4⋊Dic3—34no—
402C4⋊Dic3C22×D314yes—
403C4⋊Dic3C22×D314yes—
404C4⋊Dic3C22×D314yes—
405C4⋊Dic3C22×D314yes—
406Dic3⋊C4—34no—
407Dic3⋊C4—34no—
408Dic3⋊C4—34no—
409Dic3⋊C4—34no—
410Dic3⋊C4—34no—
411Dic3⋊C4—34no—
412Dic3⋊C4—34no—
413Dic3⋊C4—34no—
414Dic3⋊C4—34no—
415Dic3⋊C4—34no—
416Dic3⋊C4—34no—
417Dic3⋊C4—34no—
418Dic3⋊C4—34no—
419Dic3⋊C4—34no—
420Dic3⋊C4—64no—
421Dic3⋊C4—64no—
422Dic3⋊C4C22×D314yes—
423Dic3⋊C4C22×D314yes—
424Dic3⋊C4C22×D314yes—
425Dic3⋊C4C22×D314yes—
426Dic3⋊C4C22×D314yes—
427Dic3⋊C4C22×D314yes—
428C4×Dic3—34no—
429C4×Dic3—34no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—34no—
433C4×Dic3—34no—
434C4×Dic3—34no—
435C4×Dic3—34no—
436C4×Dic3C22×D314yes—
437C4×Dic3C22×D314yes—
438C22×C32C2×#4112yes—
439C22×C322−1+412yes—
440C22×C322−1+412yes—
441C22×C32C2511yescharacteristic
442C2×C3⋊D3—22no—
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—44no—
446C32×C4—22no—
447C32×C4—22no—
448C32×C4—22no—
449C3⋊Dic3—22no—
450C3⋊Dic3—22no—
451C3⋊Dic3C2×#4114yes—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
460C22×Q8—91no—
461C22×Q8—91no—
462C23×C4—91no—
463C4⋊Q8—98no—
464#126—98no—
465#126—98no—
466#126—98no—
467#126—98no—
468#125—38no—
469#125—38no—
470#125—98no—
471#125—98no—
472#125—98no—
473C22⋊Q8—98no—
474C22⋊Q8—98no—
475C4×Q8—98no—
476C4×Q8—98no—
477#117—98no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4D3211yescharacteristic
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—91no—
507C2×C42—91no—
508C2×C42—91no—
509C2×C42—91no—
510C23×C3—21no—
511C23×C3C23×D311yescharacteristic
512C23×C3C23×D311yescharacteristic
513C22×D3—32no—
514C22×D3—32no—
515C22×D3—62no—
516C22×D3—64no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—62no—
521C22×D3—62no—
522C22×D3—62no—
523C22×D3—122no—
524C22×D3—122no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—62no—
546C2×C3×C4—62no—
547C2×C3×C4—62no—
548C2×C3×C4—62no—
549C2×C3×C4—62no—
550C2×C3×C4—62no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4C23×D312yes—
554C2×C3×C4C23×D312yes—
555C2×C3×C4C23×D312yes—
556C2×C3×C4C23×D312yes—
557C2×C3×C4C23×D312yes—
558C2×C3×C4C23×D312yes—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—34no—
568C2×Dic3—34no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—64no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—62no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—62no—
583C2×Dic3—122no—
584C2×Dic3—122no—
585C2×Dic3C23×D312yes—
586C2×Dic3C23×D312yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D312yes—
589C2×Dic3C23×D312yes—
590C2×Dic3C23×D312yes—
591C2×Dic3C23×D312yes—
592C2×Dic3C23×D312yes—
593C4×D3—68no—
594C4×D3—68no—
595C4×D3—128no—
596Dic6—68no—
597Dic6—68no—
598Dic6—68no—
599Dic6—68no—
600Dic6—128no—
601C2×C32#54114yescomplemented
602C2×C32C22×#4111yescharacteristic
603C2×C32C2×2−1+411yescharacteristic
604C2×C32C2×2−1+411yescharacteristic
605C3⋊D3—42no—
606C24—91no—
607C2×Q8—94no—
608C2×Q8—94no—
609C2×Q8—184no—
610C2×Q8—184no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—91no—
620C22×C4—91no—
621C22×C4—91no—
622C22×C4—94no—
623C22×C4—184no—
624C22×C4C2×D3211yescharacteristic
625C22×C4C2×D3211yescharacteristic
626C22×C4C2×D3211yescharacteristic
627C4⋊C4—34no—
628C4⋊C4—34no—
629C4⋊C4—34no—
630C4⋊C4—34no—
631C4⋊C4—34no—
632C4⋊C4—34no—
633C4⋊C4—34no—
634C4⋊C4—34no—
635C4⋊C4—34no—
636C4⋊C4—34no—
637C4⋊C4—94no—
638C4⋊C4—94no—
639C4⋊C4—94no—
640C4⋊C4—94no—
641C4⋊C4—94no—
642C4⋊C4—94no—
643C4⋊C4—94no—
644C4⋊C4—94no—
645C4⋊C4—94no—
646C4⋊C4C2×D3214yes—
647C22⋊C4—94no—
648C22⋊C4—94no—
649C22⋊C4—94no—
650C22⋊C4—94no—
651C22⋊C4—94no—
652C22⋊C4—94no—
653C42—34no—
654C42—34no—
655C42—94no—
656C42—94no—
657C42—94no—
658C42—94no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3#100712yes—
664C22×C3#100712yes—
665C22×C3D3×#4112yes—
666C22×C3D3×#4112yes—
667C22×C3#101012yes—
668C22×C3#101012yes—
669C22×C3C24×D311yescharacteristic
670C22×C3C24×D311yescharacteristic
671C2×D3—64no—
672C2×D3—62no—
673C2×D3—62no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—128no—
681C2×D3—124no—
682C2×D3—124no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—62no—
695C3×C4—62no—
696C3×C4—62no—
697C3×C4—62no—
698C3×C4—62no—
699C3×C4—62no—
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—22no—
704Dic3—22no—
705Dic3—22no—
706Dic3—22no—
707Dic3—22no—
708Dic3—34no—
709Dic3—34no—
710Dic3—64no—
711Dic3—62no—
712Dic3—62no—
713Dic3—62no—
714Dic3—62no—
715Dic3—122no—
716Dic3—122no—
717C32C2×#54111yescharacteristic, complemented, Sylow
718C23—92no—
719C23—182no—
720C23—182no—
721C23—182no—
722C23C22×D3211yescharacteristic
723Q8—188no—
724Q8—188no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—62no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—94no—
745C2×C4—92no—
746C2×C4—92no—
747C2×C4—92no—
748C2×C4—188no—
749C2×C4—182no—
750C2×C4—182no—
751C2×C4C22×D3212yes—
752C2×C4C22×D3212yes—
753C2×C4C22×D3212yes—
754C2×C3—24no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3#569614yescomplemented
759C2×C3#569614yescomplemented
760C2×C3C2×#100711yescharacteristic
761C2×C3C2×#100711yescharacteristic
762C2×C3C2×D3×#4111yescharacteristic
763C2×C3C2×D3×#4111yescharacteristic
764C2×C3C2×#101011yescharacteristic
765C2×C3C2×#101011yescharacteristic
766D3—124no—
767D3—122no—
768D3—122no—
769C22—182no—
770C22—182no—
771C22—182no—
772C22—364no—
773C22#6429712yes—
774C22#6431212yes—
775C22#6431512yes—
776C22C23×D3211yescharacteristic
777C4—22no—
778C4—22no—
779C4—22no—
780C4—62no—
781C4—62no—
782C4—62no—
783C4—62no—
784C4—62no—
785C4—62no—
786C4—62no—
787C4—62no—
788C4—94no—
789C4—182no—
790C4—182no—
791C3—21no—
792C3C2×#569611yescharacteristic, complemented
793C3C2×#569611yescharacteristic, complemented
794C2—362no—
795C2#1059432314yesdirect product factor
796C2C2×#6429711yescharacteristic
797C2C2×#6431211yescharacteristic
798C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#890C2semidirect
3. C2×C3×#889C2semidirect
10. C2×#63847C2semidirect
11. C2×#63847C2semidirect
12. C2×#63846C2semidirect
13. C2×#63844C2semidirect
14. C2×#63840C2semidirect
15. C2×#63837C2semidirect
16. #10594323C2direct (N × H)
40. C3×#890C22semidirect
41. C3×#889C22semidirect
63. #63847C22semidirect
64. #63847C22semidirect
65. #63846C22semidirect
66. #63844C22semidirect
67. #63840C22semidirect
68. #63837C22semidirect
87. C2×#890D3semidirect
93. C2×#889D3semidirect
249. #890C2×D3semidirect
255. #889C2×D3semidirect
601. C2×C32#541semidirect
717. C32C2×#541semidirect
758. C2×C3#5696semidirect
759. C2×C3#5696semidirect
792. C3C2×#5696semidirect
793. C3C2×#5696semidirect
795. C2#10594323direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641052
C2×C3×#8902
C2×C3×#8892
C2×#638682
C2×#638652
C2×#638492
C2×#638482
C2×#638472
C2×#638462
C2×#638442
C2×#638402
C2×#638372
#105943232
C2×#56963