Finite Group Databasebeta

← C2×#10594320 #11901595

Subgroups — C2×#10594320 #11901595

Order 1152.

2131 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic
2C2×C3×#890C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×#63918C211yesmaximal, characteristic, complemented
5C2×#63895C211yesmaximal, characteristic
6C2×#63895C211yesmaximal, characteristic
7C2×#63872C211yesmaximal, characteristic, complemented
8C2×#63868C211yesmaximal, characteristic
9C2×#63848C211yesmaximal, characteristic
10C2×#63848C211yesmaximal, characteristic
11C2×#63846C211yesmaximal, characteristic, complemented
12C2×#63845C211yesmaximal, characteristic, complemented
13C2×#63838C211yesmaximal, characteristic, complemented
14C2×#63837C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic
16#10594320C2116yesmaximal, direct product factor
17C2×#5698—31nomaximal
18C2×#5696—31nomaximal
19C22×#627C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64107C2218yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#890C2218yescomplemented
43C3×#889C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63918C2218yescomplemented
58#63895C2218yes—
59#63895C2218yes—
60#63872C2218yescomplemented
61#63868C2218yes—
62#63848C2218yes—
63#63848C2218yes—
64#63846C2218yescomplemented
65#63845C2218yescomplemented
66#63838C2218yescomplemented
67#63837C2218yescomplemented
68#63836C2218yes—
69C2×C3×#125—31no—
70C2×C3×#125—31no—
71#5698—316no—
72#5696—316no—
73C2×#898—31no—
74C2×#898—31no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#898—31no—
80C2×#898—61no—
81C2×#897—31no—
82C2×#897—31no—
83C2×#896—31no—
84C2×#896—31no—
85C2×#892—31no—
86C2×#890—31no—
87C2×#890—31no—
88C2×#890—31no—
89C2×#890—31no—
90C2×#890D311yescharacteristic, complemented
91C2×#889—31no—
92C2×#889—31no—
93C2×#889D311yescharacteristic, complemented
94C2×#888—31no—
95C2×#887—31no—
96C2×#887—31no—
97C2×#887—31no—
98C2×#876—31no—
99C2×#872—31no—
100C2×#869—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
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×#627—24no—
118C2×#627—24no—
119C2×#627C2314yes—
120C2×#627C2314yes—
121C2×#624—24no—
122C2×#624C2314yes—
123C32×C4⋊C4C2314yes—
124#3752C2314yes—
125#3752C2314yes—
126#3752C2314yes—
127C4⋊(C3⋊Dic3)C2314yes—
128#3750C2314yes—
129C4×C3⋊Dic3C2314yes—
130C3×C4⋊Dic3C2314yes—
131C3×C4⋊Dic3C2314yes—
132C3×C4⋊Dic3C2314yes—
133C3×C4⋊Dic3C2314yes—
134C3×Dic3⋊C4C2314yes—
135C3×Dic3⋊C4C2314yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2314yes—
141C3×C4×Dic3C2314yes—
142#3724C2314yes—
143Dic3⋊Dic3C2314yes—
144Dic3⋊Dic3C2314yes—
145Dic3⋊Dic3C2314yes—
146Dic3⋊Dic3C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149#3722C2314yes—
150#3722C2314yes—
151#3722C2314yes—
152Dic32C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155C2×#541—91noSylow
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—31no—
161C22×Dic6—31no—
162C3×#125—38no—
163C3×#125—38no—
164C2×C3×C4⋊C4—21no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
176C2×C3×C4⋊C4C2×D311yescharacteristic
177C2×C3×C42—31no—
178C2×C3×C42—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—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—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—61no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—31no—
202C2×C4⋊Dic3—61no—
203C2×C4⋊Dic3C2×D311yescharacteristic
204C2×C4⋊Dic3C2×D311yescharacteristic
205C2×C4⋊Dic3C2×D311yescharacteristic
206C2×C4⋊Dic3C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×Dic3⋊C4C2×D311yescharacteristic
222C2×Dic3⋊C4C2×D311yescharacteristic
223C2×Dic3⋊C4C2×D311yescharacteristic
224C2×C4×Dic3—31no—
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—61no—
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#898—38no—
242#898—68no—
243#897—38no—
244#897—38no—
245#896—38no—
246#896—38no—
247#892—38no—
248#890—38no—
249#890—38no—
250#890—38no—
251#890—38no—
252#890C2×D318yescomplemented
253#889—38no—
254#889—38no—
255#889C2×D318yescomplemented
256#888—38no—
257#887—38no—
258#887—38no—
259#887—38no—
260#876—38no—
261#872—38no—
262#869—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—22no—
278C2×C3⋊Dic3C2412yes—
279C2×C3⋊Dic3C2412yes—
280C2×C3⋊Dic3C2412yes—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—22no—
285C2×C3×Dic3—22no—
286C2×C3×Dic3—22no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3#4114yes—
289C2×C3×Dic3C2412yes—
290C2×C3×Dic3C2412yes—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297#627—28no—
298#627—28no—
299#624—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×Dic6—34no—
358C2×Dic6—34no—
359C2×Dic6—34no—
360C2×Dic6—34no—
361C2×Dic6—64no—
362C2×Dic6—64no—
363C2×Dic6—64no—
364C2×Dic6—64no—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—34no—
367C3×C4⋊C4—34no—
368C3×C4⋊C4—34no—
369C3×C4⋊C4—34no—
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⋊C4C22×D314yes—
377C3×C4⋊C4C22×D314yes—
378C3×C42—34no—
379C3×C42—34no—
380(C2×D3)⋊C4—34no—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—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—64no—
393(C2×D3)⋊C4—64no—
394(C2×D3)⋊C4—64no—
395C4⋊Dic3—34no—
396C4⋊Dic3—34no—
397C4⋊Dic3—34no—
398C4⋊Dic3—34no—
399C4⋊Dic3—34no—
400C4⋊Dic3—34no—
401C4⋊Dic3—34no—
402C4⋊Dic3—34no—
403C4⋊Dic3—64no—
404C4⋊Dic3C22×D314yes—
405C4⋊Dic3C22×D314yes—
406C4⋊Dic3C22×D314yes—
407C4⋊Dic3C22×D314yes—
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—64no—
419Dic3⋊C4C22×D314yes—
420Dic3⋊C4C22×D314yes—
421Dic3⋊C4C22×D314yes—
422Dic3⋊C4C22×D314yes—
423Dic3⋊C4C22×D314yes—
424Dic3⋊C4C22×D314yes—
425C4×Dic3—34no—
426C4×Dic3—34no—
427C4×Dic3—34no—
428C4×Dic3—34no—
429C4×Dic3—34no—
430C4×Dic3—34no—
431C4×Dic3—34no—
432C4×Dic3—34no—
433C4×Dic3—64no—
434C4×Dic3C22×D314yes—
435C4×Dic3C22×D314yes—
436C22×C32C2×#4112yes—
437C22×C322−1+412yes—
438C22×C322−1+412yes—
439C22×C32C2511yescharacteristic
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—44no—
444C32×C4—22no—
445C32×C4—22no—
446C32×C4—22no—
447C3⋊Dic3—22no—
448C3⋊Dic3—22no—
449C3⋊Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—22no—
457C3×Dic3C2×#4114yes—
458C22×Q8—91no—
459C22×Q8—91no—
460C23×C4—91no—
461C4⋊Q8—98no—
462#126—98no—
463#126—98no—
464#126—98no—
465#126—98no—
466#125—38no—
467#125—38no—
468#125—98no—
469#125—98no—
470#125—98no—
471C22⋊Q8—98no—
472C22⋊Q8—98no—
473C4×Q8—98no—
474C4×Q8—98no—
475#117—98no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—31no—
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—91no—
487C2×C4⋊C4—91no—
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⋊C4D3211yescharacteristic
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C42—31no—
503C2×C42—31no—
504C2×C42—91no—
505C2×C42—91no—
506C2×C42—91no—
507C2×C42—91no—
508C23×C3—21no—
509C23×C3C23×D311yescharacteristic
510C23×C3C23×D311yescharacteristic
511C22×D3—32no—
512C22×D3—32no—
513C22×D3—62no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—62no—
517C22×D3—62no—
518C22×D3—62no—
519C22×D3—62no—
520C22×D3—122no—
521C22×D3—122no—
522C22×D3—122no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
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—34no—
533C2×C3×C4—32no—
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—42no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—62no—
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×C4C23×D312yes—
552C2×C3×C4C23×D312yes—
553C2×C3×C4C23×D312yes—
554C2×C3×C4C23×D312yes—
555C2×C3×C4C23×D312yes—
556C2×C3×C4C23×D312yes—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—62no—
571C2×Dic3—62no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—62no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3—122no—
582C2×Dic3#23914yes—
583C2×Dic3C23×D312yes—
584C2×Dic3C23×D312yes—
585C2×Dic3C23×D312yes—
586C2×Dic3C23×D312yes—
587C2×Dic3C23×D312yes—
588C2×Dic3C23×D312yes—
589C2×Dic3C23×D312yes—
590C2×Dic3C23×D312yes—
591C4×D3—68no—
592C4×D3—68no—
593Dic6—68no—
594Dic6—68no—
595Dic6—68no—
596Dic6—68no—
597C2×C32#54114yescomplemented
598C2×C32C22×#4111yescharacteristic
599C2×C32C2×2−1+411yescharacteristic
600C2×C32C2×2−1+411yescharacteristic
601C3⋊D3—42no—
602C24—91no—
603C2×Q8—94no—
604C2×Q8—94no—
605C2×Q8—184no—
606C2×Q8—184no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—94no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—184no—
620C22×C4C2×D3211yescharacteristic
621C22×C4C2×D3211yescharacteristic
622C22×C4C2×D3211yescharacteristic
623C4⋊C4—34no—
624C4⋊C4—34no—
625C4⋊C4—34no—
626C4⋊C4—34no—
627C4⋊C4—34no—
628C4⋊C4—34no—
629C4⋊C4—34no—
630C4⋊C4—34no—
631C4⋊C4—34no—
632C4⋊C4—34no—
633C4⋊C4—94no—
634C4⋊C4—94no—
635C4⋊C4—94no—
636C4⋊C4—94no—
637C4⋊C4—94no—
638C4⋊C4—94no—
639C4⋊C4—94no—
640C4⋊C4—94no—
641C4⋊C4—94no—
642C4⋊C4C2×D3214yes—
643C22⋊C4—94no—
644C22⋊C4—94no—
645C22⋊C4—94no—
646C22⋊C4—94no—
647C22⋊C4—94no—
648C22⋊C4—94no—
649C42—34no—
650C42—34no—
651C42—94no—
652C42—94no—
653C42—94no—
654C42—94no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—21no—
659C22×C3C2×#23912yes—
660C22×C3#100712yes—
661C22×C3D3×#4112yes—
662C22×C3#101012yes—
663C22×C3#101012yes—
664C22×C3#101012yes—
665C22×C3C24×D311yescharacteristic
666C22×C3C24×D311yescharacteristic
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—122no—
676C2×D3—124no—
677C2×D3—124no—
678C2×D3—244no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—34no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—62no—
695C3×C4—62no—
696Dic3—22no—
697Dic3—22no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—62no—
704Dic3—62no—
705Dic3—62no—
706Dic3—62no—
707Dic3—62no—
708Dic3—62no—
709Dic3—122no—
710Dic3—122no—
711Dic3—122no—
712Dic3C2×#23914yes—
713C32C2×#54111yescharacteristic, complemented, Sylow
714C23—92no—
715C23—182no—
716C23—182no—
717C23—182no—
718C23C22×D3211yescharacteristic
719Q8—188no—
720Q8—188no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—34no—
725C2×C4—32no—
726C2×C4—32no—
727C2×C4—32no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—92no—
743C2×C4—188no—
744C2×C4—182no—
745C2×C4—182no—
746C2×C4—182no—
747C2×C4C22×D3212yes—
748C2×C4C22×D3212yes—
749C2×C4C22×D3212yes—
750C2×C3—24no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3#569614yescomplemented
755C2×C3#569814yescomplemented
756C2×C3C22×#23911yescharacteristic
757C2×C3C2×#100711yescharacteristic
758C2×C3C2×D3×#4111yescharacteristic
759C2×C3C2×#101011yescharacteristic
760C2×C3C2×#101011yescharacteristic
761C2×C3C2×#101011yescharacteristic
762D3—122no—
763D3—122no—
764D3—242no—
765C22—182no—
766C22—182no—
767C22—182no—
768C22—364no—
769C22#6429712yes—
770C22#6430912yes—
771C22D3×#23912yes—
772C22C23×D3211yescharacteristic
773C4—22no—
774C4—22no—
775C4—22no—
776C4—34no—
777C4—62no—
778C4—62no—
779C4—62no—
780C4—62no—
781C4—62no—
782C4—62no—
783C4—62no—
784C4—182no—
785C4—182no—
786C4—182no—
787C3—21no—
788C3C2×#569611yescharacteristic, complemented
789C3C2×#569811yescharacteristic, complemented
790C2—362no—
791C2#1059432014yesdirect product factor
792C2C2×#6429711yescharacteristic
793C2C2×#6430911yescharacteristic
794C2C2×D3×#23911yescharacteristic
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
4. C2×#63918C2semidirect
7. C2×#63872C2semidirect
11. C2×#63846C2semidirect
12. C2×#63845C2semidirect
13. C2×#63838C2semidirect
14. C2×#63837C2semidirect
16. #10594320C2direct (N × H)
42. C3×#890C22semidirect
43. C3×#889C22semidirect
57. #63918C22semidirect
60. #63872C22semidirect
64. #63846C22semidirect
65. #63845C22semidirect
66. #63838C22semidirect
67. #63837C22semidirect
90. C2×#890D3semidirect
93. C2×#889D3semidirect
252. #890C2×D3semidirect
255. #889C2×D3semidirect
597. C2×C32#541semidirect
713. C32C2×#541semidirect
754. C2×C3#5696semidirect
755. C2×C3#5698semidirect
788. C3C2×#5696semidirect
789. C3C2×#5698semidirect
791. C2#10594320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×#8902
C2×C3×#8892
C2×#639182
C2×#638952
C2×#638722
C2×#638682
C2×#638482
C2×#638462
C2×#638452
C2×#638382
C2×#638372
C2×#638362
#105943202
C2×#56983
C2×#56963