Finite Group Databasebeta

← C2×#10594109 #11903326

Subgroups — C2×#10594109 #11903326

Order 1152.

2693 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C2×#63978C211yesmaximal, characteristic, complemented
5C2×#63971C211yesmaximal, characteristic, complemented
6C2×#63953C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×#63881C211yesmaximal, characteristic, complemented
10C2×#63877C211yesmaximal, characteristic, complemented
11C2×#63874C211yesmaximal, characteristic, complemented
12C2×#63864C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594109C2116yesmaximal, direct product factor
17C2×#5670—31nomaximal
18C2×#5532—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#624C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34#64093C2218yescomplemented
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#885C2218yescomplemented
45C3×#877C2218yescomplemented
46#63978C2218yescomplemented
47#63971C2218yescomplemented
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59#63953C2218yescomplemented
60#63952C2218yescomplemented
61#63910C2218yescomplemented
62#63881C2218yescomplemented
63#63877C2218yescomplemented
64#63874C2218yescomplemented
65#63864C2218yescomplemented
66#63852C2218yescomplemented
67#63839C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#117—31no—
71C2×#947—31no—
72C2×#944—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#930—31no—
76C2×C4×#67—31no—
77#5670—316no—
78#5532—316no—
79C2×#895—31no—
80C2×#893—31no—
81C2×#892—31no—
82C2×#888—31no—
83C2×#885—31no—
84C2×#885—31no—
85C2×#885—31no—
86C2×#885D311yescharacteristic, complemented
87C2×#884—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—61no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#877—31no—
95C2×#877D311yescharacteristic, complemented
96C2×#875—31no—
97C2×#875—31no—
98C2×#872—31no—
99C2×#872—31no—
100C2×#872—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×#638—24no—
109C2×#638—42no—
110C2×#638C2314yes—
111C2×#638C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4⋊(C3⋊D3)—42no—
115C2×C4⋊(C3⋊D3)C2314yes—
116C2×C4×C3⋊D3—24no—
117C2×C4×C3⋊D3C2314yes—
118C2×C3×#67—42no—
119C2×C3×#67C2314yes—
120C22×C3×Dic3—24no—
121C22×C3×Dic3C2314yes—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×Dic6—42no—
130C2×C3×Dic6C2314yes—
131C2×#627—42no—
132C2×#627C2314yes—
133C2×#626—24no—
134C2×#626—42no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#624—24no—
138C2×#624C2314yes—
139C2×D3×Dic3—24no—
140C2×D3×Dic3C2314yes—
141C32×C22⋊C4C2314yes—
142#3752C2314yes—
143#3750C2314yes—
144C3×#217C2314yes—
145C3×#217C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2314yes—
153#3724C2314yes—
154#3724C2314yes—
155Dic3⋊Dic3C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#555—91noSylow
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—61no—
175C22×#67—61no—
176C22×#67C2×D311yescharacteristic
177C23×Dic3—31no—
178C23×Dic3C2×D311yescharacteristic
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—61no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—61no—
190C22×Dic6—31no—
191C22×Dic6—31no—
192C22×Dic6C2×D311yescharacteristic
193C3×#124—38no—
194C3×#117—38no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C22⋊C4—21no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4C2×D311yescharacteristic
203C2×C3×C22⋊C4C2×D311yescharacteristic
204C2×C3×C42—31no—
205C2×C3×C42—31no—
206C2×C3×C42—31no—
207C2×#217—31no—
208C2×#217C2×D311yescharacteristic
209C2×#217C2×D311yescharacteristic
210#947—38no—
211#944—38no—
212#939—38no—
213#939—38no—
214#930—38no—
215C4×#67—38no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
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—61no—
230C2×(C2×D3)⋊C4C2×D311yescharacteristic
231C2×(C2×D3)⋊C4C2×D311yescharacteristic
232C2×C4⋊Dic3—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3C2×D311yescharacteristic
248C2×C4×Dic3C2×D311yescharacteristic
249C2×C4×Dic3C2×D311yescharacteristic
250#895—38no—
251#893—38no—
252#892—38no—
253#888—38no—
254#885—38no—
255#885—38no—
256#885—38no—
257#885C2×D318yescomplemented
258#884—38no—
259#884—38no—
260#884—38no—
261#884—38no—
262#884—68no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#877—38no—
266#877C2×D318yescomplemented
267#875—38no—
268#875—38no—
269#872—38no—
270#872—38no—
271#872—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3C2412yes—
285C22×C3⋊D3C2412yes—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294#638—28no—
295#638—44no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3#4114yes—
298C2×C3⋊Dic3C2412yes—
299C2×C3⋊Dic3C2412yes—
300C4⋊(C3⋊D3)—44no—
301C4×C3⋊D3—28no—
302C3×#67—44no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—28no—
310C2×C3×Dic3#4114yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C3×Dic6—44no—
319#627—44no—
320#626—28no—
321#626—44no—
322#624—28no—
323D3×Dic3—28no—
324#555—916no—
325C2×C4⋊Q8—91no—
326C2×#124—31no—
327C2×#124—91no—
328C2×#124—91no—
329C2×#124—91no—
330C2×#121—91no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—91no—
335C2×C4×D4—91no—
336C2×#117—31no—
337C2×#117—91no—
338C2×#117—91no—
339C2×#117—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3C22×D311yescharacteristic
343C24×C3C22×D311yescharacteristic
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—61no—
349C23×D3—61no—
350C23×D3C22×D311yescharacteristic
351C2×C3×Q8—34no—
352C2×C3×Q8—122no—
353C2×C3×D4—34no—
354C2×C3×D4—122no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—34no—
365C22×C3×C4—64no—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—42no—
377C2×#67—64no—
378C2×#67—64no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—64no—
382C2×#67—124no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67—122no—
386C2×#67—124no—
387C2×#67C22×D314yes—
388C22×Dic3—24no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—34no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—64no—
397C22×Dic3C22×D314yes—
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—64no—
410C2×D12—64no—
411C2×D12—122no—
412C2×D12—122no—
413C2×D12—124no—
414C2×D12—122no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—64no—
423C2×C4×D3—64no—
424C2×C4×D3—64no—
425C2×C4×D3—64no—
426C2×C4×D3—124no—
427C2×Dic6—34no—
428C2×Dic6—34no—
429C2×Dic6—42no—
430C2×Dic6—122no—
431C2×Dic6—122no—
432C2×Dic6C22×D314yes—
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⋊C4—34no—
440C3×C22⋊C4C22×D314yes—
441C3×C22⋊C4C22×D314yes—
442C3×C42—34no—
443C3×C42—34no—
444C3×C42—34no—
445#217—34no—
446#217C22×D314yes—
447#217C22×D314yes—
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—64no—
462(C2×D3)⋊C4C22×D314yes—
463(C2×D3)⋊C4C22×D314yes—
464C4⋊Dic3—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—64no—
473Dic3⋊C4C22×D314yes—
474Dic3⋊C4C22×D314yes—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3C22×D314yes—
480C4×Dic3C22×D314yes—
481C4×Dic3C22×D314yes—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—44no—
486C22×C32C2×#4112yes—
487C22×C32C2×#4112yes—
488C22×C32H(5,𝔽2)12yes—
489C22×C32C2511yescharacteristic
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—22no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—44no—
497C2×C3⋊D3—44no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—44no—
502C32×C4—22no—
503C32×C4—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3C2×#4114yes—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3C2×#4114yes—
513C22×Q8—31no—
514C22×Q8—91no—
515C22×D4—31no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C22×D4—91no—
520C22×D4—91no—
521C23×C4—31no—
522C23×C4—91no—
523C23×C4—91no—
524C23×C4—91no—
525C4⋊Q8—98no—
526#124—38no—
527#124—98no—
528#124—98no—
529#124—98no—
530#121—98no—
531#121—98no—
532#121—98no—
533#121—98no—
534C4×D4—98no—
535C4×D4—98no—
536#117—38no—
537#117—98no—
538#117—98no—
539#117—98no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C22⋊C4—31no—
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—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4D3211yescharacteristic
558C2×C42—31no—
559C2×C42—31no—
560C2×C42—31no—
561C2×C42—91no—
562C2×C42—91no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—21no—
571C23×C3—32no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—42no—
575C23×C3—62no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3C23×D312yes—
579C23×C3C23×D312yes—
580C23×C3C23×D311yescharacteristic
581C23×C3C23×D311yescharacteristic
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—64no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—62no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3C23×D312yes—
610C3×Q8—124no—
611C3×D4—124no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—34no—
619C2×C3×C4—32no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—68no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4C23×D312yes—
636C2×C3×C4C23×D312yes—
637C2×C3×C4C23×D312yes—
638C2×C3×C4C23×D312yes—
639#67—44no—
640#67—68no—
641#67—68no—
642#67—68no—
643#67—128no—
644#67—124no—
645#67—124no—
646#67—124no—
647#67—128no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—28no—
655C2×Dic3—34no—
656C2×Dic3—34no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—64no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—68no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—122no—
668C2×Dic3#23514yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676D12—68no—
677D12—124no—
678D12—124no—
679D12—128no—
680D12—124no—
681C4×D3—68no—
682C4×D3—68no—
683C4×D3—68no—
684C4×D3—68no—
685C4×D3—68no—
686C4×D3—128no—
687Dic6—44no—
688Dic6—124no—
689Dic6—124no—
690C2×C32—42no—
691C2×C32#55514yescomplemented
692C2×C32C22×#4111yescharacteristic
693C2×C32C22×#4111yescharacteristic
694C2×C32C2×H(5,𝔽2)11yescharacteristic
695C3⋊D3—42no—
696C3⋊D3—42no—
697C3×D3—42no—
698C24—31no—
699C24—91no—
700C24—91no—
701C24C2×D3211yescharacteristic
702C2×Q8—34no—
703C2×Q8—94no—
704C2×Q8—122no—
705C2×Q8—362no—
706C2×D4—34no—
707C2×D4—94no—
708C2×D4—94no—
709C2×D4—94no—
710C2×D4—94no—
711C2×D4—94no—
712C2×D4—122no—
713C2×D4—184no—
714C2×D4—184no—
715C2×D4—362no—
716C2×D4—362no—
717C2×D4—362no—
718C22×C4—31no—
719C22×C4—34no—
720C22×C4—31no—
721C22×C4—31no—
722C22×C4—31no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—31no—
726C22×C4—64no—
727C22×C4—94no—
728C22×C4—94no—
729C22×C4—91no—
730C22×C4—91no—
731C22×C4—94no—
732C22×C4—184no—
733C22×C4—184no—
734C22×C4—184no—
735C22×C4C2×D3211yescharacteristic
736C22×C4C2×D3211yescharacteristic
737C4⋊C4—34no—
738C4⋊C4—34no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4C2×D3214yes—
755C42—34no—
756C42—34no—
757C42—34no—
758C42—94no—
759C42—94no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—21no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—44no—
774C22×C3—44no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—84no—
779C22×C3—124no—
780C22×C3C2×#23512yes—
781C22×C3#100412yes—
782C22×C3D3×#4112yes—
783C22×C3D3×#4112yes—
784C22×C3D3×#4112yes—
785C22×C3#100912yes—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—44no—
792C2×D3—64no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—122no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—128no—
811C2×D3—124no—
812C2×D3—124no—
813C2×D3—124no—
814C2×D3—124no—
815C2×D3—244no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—34no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—22no—
835Dic3—34no—
836Dic3—34no—
837Dic3—64no—
838Dic3—62no—
839Dic3—62no—
840Dic3—122no—
841Dic3C2×#23514yes—
842C32C2×#55511yescharacteristic, complemented, Sylow
843C23—22no—
844C23—22no—
845C23—22no—
846C23—32no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—92no—
851C23—92no—
852C23—182no—
853C23—182no—
854C23—182no—
855C23—182no—
856C23—182no—
857C23—182no—
858C23C22×D3212yes—
859C23C22×D3211yescharacteristic
860Q8—124no—
861Q8—364no—
862D4—124no—
863D4—188no—
864D4—188no—
865D4—364no—
866D4—364no—
867D4—364no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—34no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—68no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—62no—
884C2×C4—62no—
885C2×C4—94no—
886C2×C4—92no—
887C2×C4—92no—
888C2×C4—188no—
889C2×C4—188no—
890C2×C4—188no—
891C2×C4—182no—
892C2×C4C22×D3212yes—
893C2×C4C22×D3212yes—
894C2×C3—21no—
895C2×C3—24no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—42no—
899C2×C3—42no—
900C2×C3—82no—
901C2×C3—122no—
902C2×C3#553214yescomplemented
903C2×C3#567014yescomplemented
904C2×C3C22×#23511yescharacteristic
905C2×C3C2×#100411yescharacteristic
906C2×C3C2×D3×#4111yescharacteristic
907C2×C3C2×D3×#4111yescharacteristic
908C2×C3C2×D3×#4111yescharacteristic
909C2×C3C2×#100911yescharacteristic
910D3—42no—
911D3—124no—
912D3—122no—
913D3—122no—
914D3—122no—
915D3—122no—
916D3—242no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—44no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—124no—
925C22—182no—
926C22—182no—
927C22—182no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—364no—
932C22—364no—
933C22D3×#23512yes—
934C22#6431212yes—
935C22#6431412yes—
936C22C23×D3211yescharacteristic
937C4—22no—
938C4—22no—
939C4—34no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—94no—
947C4—182no—
948C3—21no—
949C3C2×#553211yescharacteristic, complemented
950C3C2×#567011yescharacteristic, complemented
951C2—42no—
952C2—122no—
953C2—362no—
954C2—362no—
955C2#1059410914yesdirect product factor
956C2C2×D3×#23511yescharacteristic
957C2C2×#6431211yescharacteristic
958C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#555
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×#64093C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#877C2semidirect
4. C2×#63978C2semidirect
5. C2×#63971C2semidirect
6. C2×#63953C2semidirect
7. C2×#63952C2semidirect
8. C2×#63910C2semidirect
9. C2×#63881C2semidirect
10. C2×#63877C2semidirect
11. C2×#63874C2semidirect
12. C2×#63864C2semidirect
13. C2×#63852C2semidirect
14. C2×#63839C2semidirect
15. C2×#63836C2semidirect
16. #10594109C2direct (N × H)
34. #64093C22semidirect
44. C3×#885C22semidirect
45. C3×#877C22semidirect
46. #63978C22semidirect
47. #63971C22semidirect
59. #63953C22semidirect
60. #63952C22semidirect
61. #63910C22semidirect
62. #63881C22semidirect
63. #63877C22semidirect
64. #63874C22semidirect
65. #63864C22semidirect
66. #63852C22semidirect
67. #63839C22semidirect
68. #63836C22semidirect
86. C2×#885D3semidirect
95. C2×#877D3semidirect
257. #885C2×D3semidirect
266. #877C2×D3semidirect
691. C2×C32#555semidirect
842. C32C2×#555semidirect
902. C2×C3#5532semidirect
903. C2×C3#5670semidirect
949. C3C2×#5532semidirect
950. C3C2×#5670semidirect
955. C2#10594109direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640932
C2×C3×#8852
C2×C3×#8772
C2×#639782
C2×#639712
C2×#639532
C2×#639522
C2×#639102
C2×#638812
C2×#638772
C2×#638742
C2×#638642
C2×#638522
C2×#638392
C2×#638362
#105941092
C2×#56703
C2×#55323