Finite Group Databasebeta

← C2×#10594035 #11901924

Subgroups — C2×#10594035 #11901924

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic
2C2×C3×#878C211yesmaximal, characteristic
3C2×C3×#877C211yesmaximal, characteristic
4C2×#63982C211yesmaximal, characteristic
5C22×Dic3⋊Dic3C211yesmaximal, characteristic
6C2×#63964C211yesmaximal, characteristic
7C2×#63955C211yesmaximal, characteristic
8C2×#63918C211yesmaximal, characteristic, complemented
9C2×#63867C211yesmaximal, characteristic, complemented
10C2×#63867C211yesmaximal, characteristic, complemented
11C2×#63866C211yesmaximal, characteristic, complemented
12C2×#63846C211yesmaximal, characteristic, complemented
13C2×#63845C211yesmaximal, characteristic, complemented
14C2×#63840C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594035C2116yesmaximal, direct product factor
17C2×#5623—31nomaximal
18C2×#5519—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31#64087C2218yes—
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#878C2218yes—
42C3×#877C2218yes—
43#63982C2218yes—
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×Dic3⋊Dic3C2218yes—
57#63964C2218yes—
58#63955C2218yes—
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63918C2218yescomplemented
62#63867C2218yescomplemented
63#63867C2218yescomplemented
64#63866C2218yescomplemented
65#63846C2218yescomplemented
66#63845C2218yescomplemented
67#63840C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×#117—31no—
71C2×#944—31no—
72C2×#944—31no—
73C2×#926—31no—
74C22×C4⋊Dic3—31no—
75C2×#924—31no—
76C22×Dic3⋊C4—31no—
77#5623—316no—
78#5519—316no—
79C2×#890—31no—
80C2×#890—31no—
81C2×#889—31no—
82C2×#889—31no—
83C2×#889—31no—
84C2×#889—31no—
85C2×#888—31no—
86C2×#888—31no—
87C2×#888—31no—
88C2×#888—31no—
89C2×#878—31no—
90C2×#878—31no—
91C2×#878—31no—
92C2×#878—31no—
93C2×#878—31no—
94C2×#878—61no—
95C2×#878D311yescharacteristic
96C2×#877—31no—
97C2×#877D311yescharacteristic
98C2×#870—31no—
99C2×#870—31no—
100C2×#869—31no—
101C2×#869—31no—
102C24×C32C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C3⋊Dic3—42no—
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2314yes—
111C2×#634—42no—
112C2×#634C2314yes—
113C22×C3×Dic3—42no—
114C22×C3×Dic3Q818yescomplemented
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2314yes—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2314yes—
125C2×C3×Dic6—42no—
126C2×C3×Dic6C2314yes—
127C2×#627—42no—
128C2×#627—42no—
129C2×#627C2314yes—
130C2×#627C2314yes—
131C32×C22⋊C4C2314yes—
132#3757C2314yes—
133C4⋊(C3⋊Dic3)C2314yes—
134#3750C2314yes—
135#3750C2314yes—
136C3×#217C2314yes—
137C3×#217C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×C4×Dic3C2314yes—
144C3×C4×Dic3C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159C2×#544—91noSylow
160C22×C3×Q8—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C23×Dic3—31no—
164C23×Dic3—31no—
165C23×Dic3—61no—
166C23×Dic3C2×D311yescharacteristic
167C23×Dic3C2×D311yescharacteristic
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6—61no—
175C22×Dic6C2×D311yescharacteristic
176C3×C22⋊Q8—38no—
177C3×#117—38no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C22⋊C4—21no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4C2×D311yescharacteristic
187C2×C3×C22⋊C4C2×D311yescharacteristic
188C2×C3×C42—31no—
189C2×C3×C42—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—61no—
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195#944—38no—
196#944—38no—
197#926—38no—
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—31no—
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—38no—
211C2×C4⋊Dic3—61no—
212C2×C4⋊Dic3C2×D311yescharacteristic
213#924—38no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—38no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3C2×D311yescharacteristic
244C2×C4×Dic3C2×D311yescharacteristic
245#890—38no—
246#890—38no—
247#889—38no—
248#889—38no—
249#889—38no—
250#889—38no—
251#888—38no—
252#888—38no—
253#888—38no—
254#888—38no—
255#878—38no—
256#878—38no—
257#878—38no—
258#878—38no—
259#878—38no—
260#878—68no—
261#878C2×D318yes—
262#877—38no—
263#877C2×D318yes—
264#870—38no—
265#870—38no—
266#869—38no—
267#869—38no—
268C23×C32—22no—
269C23×C32—22no—
270C23×C32C2×Q814yes—
271C23×C32C2412yes—
272C23×C32C2411yescharacteristic
273C2×C32×C4—22no—
274C2×C32×C4—22no—
275C2×C32×C4C2412yes—
276C2×C32×C4C2412yes—
277C2×C3⋊Dic3—22no—
278C2×C3⋊Dic3—22no—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—44no—
282C2×C3⋊Dic3C2412yes—
283C2×C3⋊Dic3C2412yes—
284C2×C3⋊Dic3C2412yes—
285C2×C3⋊Dic3C2412yes—
286#634—44no—
287C2×C3×Dic3—22no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—44no—
294C2×C3×Dic3C2×Q814yes—
295C2×C3×Dic3C2×Q814yes—
296C2×C3×Dic3C2×Q8116yescomplemented
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C3×Dic6—44no—
306#627—44no—
307#627—44no—
308#544—916no—
309C2×C4⋊Q8—91no—
310C2×C4⋊Q8—91no—
311C2×C4⋊Q8—91no—
312C2×C4⋊Q8—91no—
313C2×#125—91no—
314C2×#125—91no—
315C2×#125—91no—
316C2×#125—91no—
317C2×C22⋊Q8—31no—
318C2×C22⋊Q8—91no—
319C2×C22⋊Q8—91no—
320C2×C22⋊Q8—91no—
321C2×#117—31no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—21no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C2×C3×Q8—34no—
328C2×C3×Q8—122no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—38no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—34no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—34no—
342C22×C3×C4—122no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—34no—
356C22×Dic3—34no—
357C22×Dic3—42no—
358C22×Dic3—61no—
359C22×Dic3—64no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—122no—
364C22×Dic3—122no—
365C22×Dic3—124no—
366C22×Dic3Dic618yescomplemented
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D314yes—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D314yes—
377C2×Dic6—34no—
378C2×Dic6—34no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—42no—
384C2×Dic6—64no—
385C2×Dic6—122no—
386C2×Dic6—122no—
387C2×Dic6—122no—
388C2×Dic6—122no—
389C2×Dic6—122no—
390C2×Dic6—122no—
391C2×Dic6—124no—
392C2×Dic6C22×D314yes—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4C22×D314yes—
402C3×C22⋊C4C22×D314yes—
403C3×C42—34no—
404C3×C42—34no—
405#217—34no—
406#217—34no—
407#217—64no—
408#217C22×D314yes—
409#217C22×D314yes—
410C4⋊Dic3—34no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—64no—
423C4⋊Dic3C22×D314yes—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—64no—
443Dic3⋊C4—64no—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447Dic3⋊C4C22×D314yes—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3—34no—
452C4×Dic3C22×D314yes—
453C4×Dic3C22×D314yes—
454C22×C32—28no—
455C22×C32—22no—
456C22×C32—22no—
457C22×C32C22×Q814yes—
458C22×C32C22×Q812yes—
459C22×C32H(5,𝔽2)12yes—
460C22×C322−1+412yes—
461C22×C32C2511yescharacteristic
462C32×C4—22no—
463C32×C4—22no—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3C22×Q814yes—
475C3×Dic3C22×Q814yes—
476C22×Q8—31no—
477C22×Q8—91no—
478C22×Q8—91no—
479C22×Q8—91no—
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—91no—
483C4⋊Q8—98no—
484C4⋊Q8—98no—
485C4⋊Q8—98no—
486C4⋊Q8—98no—
487#125—98no—
488#125—98no—
489#125—98no—
490#125—98no—
491C22⋊Q8—38no—
492C22⋊Q8—98no—
493C22⋊Q8—98no—
494C22⋊Q8—98no—
495#117—38no—
496#117—98no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—98no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—91no—
514C2×C4⋊C4—91no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4D3211yescharacteristic
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—91no—
525C2×C42—91no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—21no—
532C23×C3—24no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3C2×Dic614yes—
536C23×C3D3×Q814yes—
537C23×C3C23×D312yes—
538C23×C3C23×D312yes—
539C23×C3C23×D311yescharacteristic
540C23×C3C23×D311yescharacteristic
541C3×Q8—124no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—34no—
549C2×C3×C4—34no—
550C2×C3×C4—316no—
551C2×C3×C4—32no—
552C2×C3×C4—32no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—42no—
560C2×C3×C4—42no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—124no—
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×Dic3—22no—
573C2×Dic3—22no—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—32no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—44no—
587C2×Dic3—62no—
588C2×Dic3—62no—
589C2×Dic3—62no—
590C2×Dic3—62no—
591C2×Dic3—64no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3—122no—
603C2×Dic3—124no—
604C2×Dic3—124no—
605C2×Dic3—128no—
606C2×Dic3C2×Dic614yes—
607C2×Dic3C2×Dic614yes—
608C2×Dic3C2×Dic6116yescomplemented
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617Dic6—44no—
618Dic6—124no—
619Dic6—124no—
620Dic6—124no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624Dic6—128no—
625C2×C32—24no—
626C2×C32#54414yescomplemented
627C2×C32C23×Q811yescharacteristic
628C2×C32C2×H(5,𝔽2)11yescharacteristic
629C2×C32C2×2−1+411yescharacteristic
630C24C2×D3211yescharacteristic
631C2×Q8—34no—
632C2×Q8—94no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—122no—
636C2×Q8—362no—
637C2×Q8—362no—
638C2×Q8—362no—
639C22×C4—34no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—38no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—34no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—94no—
655C22×C4—122no—
656C22×C4—362no—
657C22×C4C2×D3211yescharacteristic
658C22×C4C2×D3211yescharacteristic
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—94no—
673C4⋊C4—94no—
674C4⋊C4—94no—
675C4⋊C4—94no—
676C4⋊C4—94no—
677C4⋊C4—94no—
678C4⋊C4—94no—
679C22⋊C4—34no—
680C22⋊C4—34no—
681C22⋊C4—94no—
682C22⋊C4C2×D3214yes—
683C42—34no—
684C42—34no—
685C42—94no—
686C42—94no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—28no—
692C22×C3—28no—
693C22×C3—22no—
694C22×C3—24no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—21no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—48no—
701C22×C3C22×Dic614yes—
702C22×C3C22×Dic612yes—
703C22×C3#100412yes—
704C22×C3C2×D3×Q814yes—
705C22×C3C2×D3×Q812yes—
706C22×C3#100912yes—
707C22×C3#101012yes—
708C22×C3#101012yes—
709C22×C3C24×D311yescharacteristic
710C22×C3C24×D311yescharacteristic
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—34no—
716C3×C4—34no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—62no—
725Dic3—22no—
726Dic3—22no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—64no—
732Dic3—62no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3C22×Dic614yes—
744Dic3C22×Dic614yes—
745C32C2×#54411yescharacteristic, complemented, Sylow
746C23—22no—
747C23—22no—
748C23D3×Dic614yes—
749C23C22×D3212yes—
750C23C22×D3211yescharacteristic
751Q8—124no—
752Q8—364no—
753Q8—364no—
754Q8—364no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—34no—
758C2×C4—34no—
759C2×C4—316no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—92no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—92no—
778C2×C4—124no—
779C2×C4—182no—
780C2×C4—182no—
781C2×C4—182no—
782C2×C4—182no—
783C2×C4—364no—
784C2×C4C22×D3212yes—
785C2×C4C22×D3212yes—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—24no—
792C2×C3—44no—
793C2×C3#551914yescomplemented
794C2×C3#562314yescomplemented
795C2×C3C23×Dic611yescharacteristic
796C2×C3C2×#100411yescharacteristic
797C2×C3C22×D3×Q811yescharacteristic
798C2×C3C2×#100911yescharacteristic
799C2×C3C2×#101011yescharacteristic
800C2×C3C2×#101011yescharacteristic
801C22—22no—
802C22—22no—
803C22—28no—
804C22C2×D3×Dic614yes—
805C22C2×D3×Dic612yes—
806C22#6430912yes—
807C22#6431412yes—
808C22C23×D3211yescharacteristic
809C4—22no—
810C4—22no—
811C4—34no—
812C4—34no—
813C4—62no—
814C4—62no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—62no—
819C4—182no—
820C4—182no—
821C4—182no—
822C4—182no—
823C3—21no—
824C3C2×#551911yescharacteristic, complemented
825C3C2×#562311yescharacteristic, complemented
826C2—24no—
827C2#1059403514yesdirect product factor
828C2C22×D3×Dic611yescharacteristic
829C2C2×#6430911yescharacteristic
830C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×#63918C2semidirect
9. C2×#63867C2semidirect
10. C2×#63867C2semidirect
11. C2×#63866C2semidirect
12. C2×#63846C2semidirect
13. C2×#63845C2semidirect
14. C2×#63840C2semidirect
15. C2×#63839C2semidirect
16. #10594035C2direct (N × H)
61. #63918C22semidirect
62. #63867C22semidirect
63. #63867C22semidirect
64. #63866C22semidirect
65. #63846C22semidirect
66. #63845C22semidirect
67. #63840C22semidirect
68. #63839C22semidirect
114. C22×C3×Dic3Q8semidirect
296. C2×C3×Dic3C2×Q8semidirect
366. C22×Dic3Dic6semidirect
608. C2×Dic3C2×Dic6semidirect
626. C2×C32#544semidirect
745. C32C2×#544semidirect
793. C2×C3#5519semidirect
794. C2×C3#5623semidirect
824. C3C2×#5519semidirect
825. C3C2×#5623semidirect
827. C2#10594035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640872
C2×C3×#8782
C2×C3×#8772
C2×#639822
C22×Dic3⋊Dic32
C2×#639642
C2×#639552
C2×#639182
C2×#638672
C2×#638662
C2×#638462
C2×#638452
C2×#638402
C2×#638392
#105940352
C2×#56233
C2×#55193