Finite Group Databasebeta

← C2×#10594059 #11901154

Subgroups — C2×#10594059 #11901154

Order 1152.

3493 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63971C211yesmaximal, characteristic, complemented
9C2×#63910C211yesmaximal, characteristic, complemented
10C2×#63909C211yesmaximal, characteristic, complemented
11C2×#63899C211yesmaximal, characteristic, complemented
12C2×#63888C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×#63865C211yesmaximal, characteristic, complemented
16#10594059C2116yesmaximal, direct product factor
17C2×#5629—31nomaximal
18C2×#5597—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic
29C22×#627C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C2×#3804—28no—
36C2×#3804C2218yescomplemented
37C22×D3×Dic3C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic
40C2×#3796—28no—
41C2×#3796C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3750C2211yescharacteristic
45#64093C2218yescomplemented
46C2×C3×#217C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×C4⋊Dic3C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×Dic3⋊C4C2211yescharacteristic
52C3×#884C2218yescomplemented
53C3×#878C2218yescomplemented
54#63978C2218yescomplemented
55#63971C2218yescomplemented
56#63971C2218yescomplemented
57C2×#3724C2211yescharacteristic
58C2×#3724C2211yescharacteristic
59C2×Dic3⋊Dic3C2211yescharacteristic
60C2×#3722C2211yescharacteristic
61C2×#3722C2211yescharacteristic
62C2×#3722C2211yescharacteristic
63C2×(C2×D3)⋊Dic3C2211yescharacteristic
64#63910C2218yescomplemented
65#63909C2218yescomplemented
66#63899C2218yescomplemented
67#63888C2218yescomplemented
68#63886C2218yescomplemented
69D3×Dic3⋊C4C2218yescomplemented
70#63865C2218yescomplemented
71C22×#239—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×#235—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×#121—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939—31no—
82C2×#930—31no—
83C2×#930—31no—
84C22×Dic3⋊C4—31no—
85#5629—316no—
86#5597—316no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—31no—
90C2×#896—31no—
91C2×#895—31no—
92C2×#895—31no—
93C2×#895—31no—
94C2×D3×C4⋊C4—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#884—31no—
100C2×#884—61no—
101C2×#884D311yescharacteristic, complemented
102C2×#878—31no—
103C2×#878D311yescharacteristic, complemented
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C2×#638—24no—
112C2×#638—42no—
113C2×#638C2314yes—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4⋊(C3⋊D3)—42no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4×C3⋊D3—24no—
120C2×C4×C3⋊D3C2314yes—
121C2×C3×#67—24no—
122C2×C3×#67—42no—
123C2×C3×#67C2314yes—
124C2×C3×#67C2314yes—
125C22×C3×Dic3—24no—
126C22×C3×Dic3C2314yes—
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×D12—24no—
134C2×C3×D12C2314yes—
135C2×C3×C4×D3—42no—
136C2×C3×C4×D3C2314yes—
137C2×C3×Dic6—24no—
138C2×C3×Dic6C2314yes—
139C2×#627—24no—
140C2×#627C2314yes—
141C2×#626—24no—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626—42no—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#626C2314yes—
148C2×#626C2314yes—
149C2×#624—24no—
150C2×#624C2314yes—
151#3804—232no—
152C2×D3×Dic3—24no—
153C2×D3×Dic3—42no—
154C2×D3×Dic3D418yescomplemented
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yes—
158#3796—232no—
159C32×C22⋊C4C2314yes—
160#3752C2314yes—
161#3750C2314yes—
162C3×#217C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×C4⋊Dic3C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168#3724C2314yes—
169#3724C2314yes—
170Dic3⋊Dic3C2314yes—
171#3722C2314yes—
172#3722C2314yes—
173#3722C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175C2×#537—91noSylow
176C22×C3×Q8—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—61no—
191C22×#67—61no—
192C22×#67C2×D311yescharacteristic
193C22×#67C2×D311yescharacteristic
194C23×Dic3—31no—
195C23×Dic3—31no—
196C23×Dic3—31no—
197C23×Dic3C2×D311yescharacteristic
198C2×#239—38no—
199C2×#239—68no—
200C2×#237—38no—
201C2×#237—38no—
202C2×#237—68no—
203C2×#237—68no—
204C2×#235—38no—
205C2×#235—68no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—61no—
213C22×D12C2×D311yescharacteristic
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—61no—
222C22×C4×D3C2×D311yescharacteristic
223C22×Dic6—31no—
224C22×Dic6—31no—
225C22×Dic6C2×D311yescharacteristic
226C3×C22⋊Q8—38no—
227C3×#121—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C4⋊C4—31no—
232C2×C3×C22⋊C4—21no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4C2×D311yescharacteristic
236C2×C3×C22⋊C4C2×D311yescharacteristic
237C2×#217—31no—
238C2×#217C2×D311yescharacteristic
239#946—38no—
240#939—38no—
241#939—38no—
242#939—38no—
243#939—38no—
244#930—38no—
245#930—38no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—61no—
256C2×(C2×D3)⋊C4C2×D311yescharacteristic
257C2×C4⋊Dic3—31no—
258C2×C4⋊Dic3C2×D311yescharacteristic
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—31no—
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4—31no—
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—38no—
267C2×Dic3⋊C4—61no—
268C2×Dic3⋊C4C2×D311yescharacteristic
269C2×Dic3⋊C4C2×D311yescharacteristic
270C2×Dic3⋊C4C2×D311yescharacteristic
271#896—38no—
272#896—38no—
273#896—38no—
274#896—38no—
275#895—38no—
276#895—38no—
277#895—38no—
278D3×C4⋊C4—38no—
279#884—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#884—38no—
284#884—68no—
285#884C2×D318yescomplemented
286#878—38no—
287#878C2×D318yescomplemented
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3C2412yes—
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3C2×D414yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4C2412yes—
312C2×C32×C4C2412yes—
313#638—28no—
314#638—44no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3C2×D414yes—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C4⋊(C3⋊D3)—44no—
320C4×C3⋊D3—28no—
321C3×#67—28no—
322C3×#67—44no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—28no—
329C2×C3×Dic3C2×D414yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C3×D12—28no—
337C3×C4×D3—44no—
338C3×Dic6—28no—
339#627—28no—
340#626—28no—
341#626—28no—
342#626—28no—
343#626—44no—
344#624—28no—
345D3×Dic3—28no—
346D3×Dic3—44no—
347D3×Dic3C2×D4116yescomplemented
348C22×#41—91no—
349C22×#41—91no—
350#537—916no—
351C2×C22⋊Q8—31no—
352C2×C22⋊Q8—91no—
353C2×C22⋊Q8—91no—
354C2×C22⋊Q8—91no—
355C2×#121—31no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×#121—91no—
360C2×#121—91no—
361C2×#121—91no—
362C2×#121—91no—
363C22×C4⋊C4—91no—
364C24×C3—21no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3C22×D311yescharacteristic
368C24×C3C22×D311yescharacteristic
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—31no—
373C23×D3—61no—
374C23×D3—61no—
375C23×D3C22×D311yescharacteristic
376C23×D3C22×D311yescharacteristic
377C2×C3×Q8—34no—
378C2×C3×Q8—64no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—34no—
382C2×C3×D4—64no—
383C2×C3×D4—64no—
384C2×C3×D4—122no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—34no—
394C22×C3×C4—34no—
395C22×C3×C4—64no—
396C22×C3×C4—122no—
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C2×#67—24no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—42no—
411C2×#67—64no—
412C2×#67—64no—
413C2×#67—64no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—124no—
419C2×#67—122no—
420C2×#67—122no—
421C2×#67—122no—
422C2×#67—124no—
423C2×#67C22×D314yes—
424C2×#67C22×D314yes—
425C22×Dic3—24no—
426C22×Dic3—31no—
427C22×Dic3—31no—
428C22×Dic3—38no—
429C22×Dic3—34no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—34no—
433C22×Dic3—34no—
434C22×Dic3—61no—
435C22×Dic3—61no—
436C22×Dic3—64no—
437C22×Dic3—122no—
438C22×Dic3C22×D314yes—
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443C22×Dic3C22×D311yescharacteristic
444C22×Dic3C22×D311yescharacteristic
445#239—632no—
446#237—632no—
447#237—632no—
448#235—632no—
449C2×D12—24no—
450C2×D12—34no—
451C2×D12—34no—
452C2×D12—34no—
453C2×D12—34no—
454C2×D12—34no—
455C2×D12—34no—
456C2×D12—64no—
457C2×D12—64no—
458C2×D12—64no—
459C2×D12—64no—
460C2×D12—122no—
461C2×D12—122no—
462C2×D12—124no—
463C2×D12—122no—
464C2×D12C22×D314yes—
465C2×C4×D3—38no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—42no—
474C2×C4×D3—64no—
475C2×C4×D3—64no—
476C2×C4×D3—64no—
477C2×C4×D3—64no—
478C2×C4×D3—64no—
479C2×C4×D3—64no—
480C2×C4×D3—124no—
481C2×C4×D3—122no—
482C2×C4×D3C22×D314yes—
483C2×Dic6—24no—
484C2×Dic6—34no—
485C2×Dic6—34no—
486C2×Dic6—64no—
487C2×Dic6—64no—
488C2×Dic6C22×D314yes—
489C3×C4⋊C4—34no—
490C3×C4⋊C4—34no—
491C3×C4⋊C4—34no—
492C3×C4⋊C4—34no—
493C3×C22⋊C4—24no—
494C3×C22⋊C4—34no—
495C3×C22⋊C4—34no—
496C3×C22⋊C4C22×D314yes—
497C3×C22⋊C4C22×D314yes—
498#217—34no—
499#217C22×D314yes—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—64no—
510(C2×D3)⋊C4C22×D314yes—
511C4⋊Dic3—34no—
512C4⋊Dic3C22×D314yes—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—64no—
521Dic3⋊C4C22×D314yes—
522Dic3⋊C4C22×D314yes—
523Dic3⋊C4C22×D314yes—
524C22×C32—22no—
525C22×C32—22no—
526C22×C32—22no—
527C22×C32—44no—
528C22×C32C22×D412yes—
529C22×C32H(5,𝔽2)12yes—
530C22×C322−1+412yes—
531C22×C32C2511yescharacteristic
532C2×C3⋊D3—22no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—22no—
536C2×C3⋊D3—22no—
537C2×C3⋊D3—22no—
538C2×C3⋊D3—44no—
539C2×C3⋊D3—44no—
540C2×C3×D3—28no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—44no—
547C2×C3×D3C22×D414yes—
548C32×C4—22no—
549C32×C4—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D414yes—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3C22×D414yes—
558C2×#41—98no—
559C2×#41—98no—
560C2×#41—188no—
561C2×#41—188no—
562C22×Q8—31no—
563C22×Q8—91no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C22×D4—91no—
571C22×D4—91no—
572C22×D4—91no—
573C22×D4—91no—
574C23×C4—31no—
575C23×C4—31no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—91no—
579C23×C4—91no—
580C23×C4—91no—
581C22⋊Q8—38no—
582C22⋊Q8—98no—
583C22⋊Q8—98no—
584C22⋊Q8—98no—
585#121—38no—
586#121—98no—
587#121—98no—
588#121—98no—
589#121—98no—
590#121—98no—
591#121—98no—
592#121—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—98no—
598C2×C4⋊C4—91no—
599C2×C4⋊C4—91no—
600C2×C4⋊C4—91no—
601C2×C4⋊C4—91no—
602C2×C22⋊C4—31no—
603C2×C22⋊C4—31no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C22⋊C4D3211yescharacteristic
610C23×C3—22no—
611C23×C3—22no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—21no—
618C23×C3—34no—
619C23×C3—32no—
620C23×C3—32no—
621C23×C3—42no—
622C23×C3—42no—
623C23×C3—42no—
624C23×C3—62no—
625C23×C3—62no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3C23×D312yes—
630C23×C3C23×D312yes—
631C23×C3C23×D311yescharacteristic
632C23×C3C23×D311yescharacteristic
633C22×D3—22no—
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—22no—
638C22×D3—32no—
639C22×D3—32no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—64no—
645C22×D3—62no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—62no—
653C22×D3—62no—
654C22×D3—62no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—122no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3D3×D414yes—
663C22×D3C23×D312yes—
664C22×D3C23×D312yes—
665C3×Q8—68no—
666C3×D4—68no—
667C3×D4—68no—
668C3×D4—124no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—34no—
676C2×C3×C4—32no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—42no—
683C2×C3×C4—42no—
684C2×C3×C4—68no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—124no—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694C2×C3×C4C23×D312yes—
695#67—28no—
696#67—44no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—128no—
703#67—124no—
704#67—124no—
705#67—124no—
706#67—128no—
707C2×Dic3—22no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—28no—
713C2×Dic3—34no—
714C2×Dic3—34no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—316no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—64no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—68no—
724C2×Dic3—62no—
725C2×Dic3—62no—
726C2×Dic3—122no—
727C2×Dic3—124no—
728C2×Dic3D3×D414yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735D12—28no—
736D12—68no—
737D12—68no—
738D12—68no—
739D12—124no—
740D12—124no—
741D12—128no—
742D12—124no—
743C4×D3—316no—
744C4×D3—44no—
745C4×D3—68no—
746C4×D3—68no—
747C4×D3—68no—
748C4×D3—68no—
749C4×D3—68no—
750C4×D3—128no—
751C4×D3—124no—
752Dic6—28no—
753Dic6—68no—
754Dic6—68no—
755C2×C32—42no—
756C2×C32#53714yescomplemented
757C2×C32C23×D411yescharacteristic
758C2×C32C2×H(5,𝔽2)11yescharacteristic
759C2×C32C2×2−1+411yescharacteristic
760C3⋊D3—42no—
761C3⋊D3—42no—
762C3×D3—24no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—91no—
767C24—91no—
768C24C2×D3211yescharacteristic
769#41—1832no—
770#41—1832no—
771C2×Q8—34no—
772C2×Q8—64no—
773C2×Q8—94no—
774C2×Q8—184no—
775C2×D4—34no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—64no—
779C2×D4—64no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—122no—
788C2×D4—184no—
789C2×D4—184no—
790C2×D4—184no—
791C2×D4—184no—
792C2×D4—362no—
793C2×D4—362no—
794C2×D4—362no—
795C22×C4—31no—
796C22×C4—34no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—34no—
803C22×C4—64no—
804C22×C4—94no—
805C22×C4—94no—
806C22×C4—98no—
807C22×C4—94no—
808C22×C4—94no—
809C22×C4—91no—
810C22×C4—91no—
811C22×C4—94no—
812C22×C4—122no—
813C22×C4—184no—
814C22×C4—184no—
815C22×C4—184no—
816C22×C4—362no—
817C22×C4C2×D3211yescharacteristic
818C22×C4C2×D3211yescharacteristic
819C4⋊C4—34no—
820C4⋊C4—34no—
821C4⋊C4—34no—
822C4⋊C4—34no—
823C4⋊C4—94no—
824C4⋊C4—94no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C22⋊C4—34no—
828C22⋊C4—34no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4—94no—
832C22⋊C4—94no—
833C22⋊C4—94no—
834C22⋊C4C2×D3214yes—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—21no—
845C22×C3—34no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—44no—
850C22×C3—44no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—68no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—84no—
858C22×C3—124no—
859C22×C3C2×D3×D412yes—
860C22×C3C2×D3×D412yes—
861C22×C3#100412yes—
862C22×C3#100712yes—
863C22×C3#100912yes—
864C22×C3#101012yes—
865C22×C3C24×D311yescharacteristic
866C22×C3C24×D311yescharacteristic
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—28no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—44no—
874C2×D3—64no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—122no—
891C2×D3—122no—
892C2×D3—128no—
893C2×D3—124no—
894C2×D3—124no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—244no—
898C2×D3C2×D3×D414yes—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—34no—
904C3×C4—42no—
905C3×C4—42no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—62no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—22no—
915Dic3—22no—
916Dic3—34no—
917Dic3—34no—
918Dic3—64no—
919Dic3—62no—
920Dic3—62no—
921Dic3—122no—
922Dic3C2×D3×D414yes—
923C32C2×#53711yescharacteristic, complemented, Sylow
924C23—22no—
925C23—22no—
926C23—22no—
927C23—34no—
928C23—32no—
929C23—32no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—92no—
936C23—92no—
937C23—182no—
938C23—182no—
939C23—182no—
940C23—182no—
941C23—182no—
942C23—182no—
943C23C22×D3212yes—
944C23C22×D3211yescharacteristic
945Q8—68no—
946Q8—188no—
947D4—68no—
948D4—68no—
949D4—124no—
950D4—188no—
951D4—188no—
952D4—188no—
953D4—188no—
954D4—364no—
955D4—364no—
956D4—364no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—34no—
960C2×C4—32no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—32no—
966C2×C4—68no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—62no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—916no—
973C2×C4—94no—
974C2×C4—92no—
975C2×C4—92no—
976C2×C4—124no—
977C2×C4—188no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4—182no—
981C2×C4—364no—
982C2×C4C22×D3212yes—
983C2×C4C22×D3212yes—
984C2×C3—24no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—42no—
989C2×C3—42no—
990C2×C3—64no—
991C2×C3—82no—
992C2×C3—122no—
993C2×C3#559714yescomplemented
994C2×C3#562914yescomplemented
995C2×C3C22×D3×D411yescharacteristic
996C2×C3C22×D3×D411yescharacteristic
997C2×C3C2×#100411yescharacteristic
998C2×C3C2×#100711yescharacteristic
999C2×C3C2×#100911yescharacteristic
1000C2×C3C2×#101011yescharacteristic
1001D3—24no—
1002D3—42no—
1003D3—124no—
1004D3—122no—
1005D3—122no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—34no—
1013C22—44no—
1014C22—68no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—62no—
1020C22—124no—
1021C22—182no—
1022C22—182no—
1023C22—182no—
1024C22—182no—
1025C22—182no—
1026C22—182no—
1027C22—364no—
1028C22—364no—
1029C22#6429712yes—
1030C22D32×D412yes—
1031C22#6431412yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—22no—
1035C4—34no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—62no—
1040C4—62no—
1041C4—94no—
1042C4—182no—
1043C3—21no—
1044C3C2×#559711yescharacteristic, complemented
1045C3C2×#562911yescharacteristic, complemented
1046C2—42no—
1047C2—64no—
1048C2—122no—
1049C2—362no—
1050C2—362no—
1051C2#1059405914yesdirect product factor
1052C2C2×#6429711yescharacteristic
1053C2C2×D32×D411yescharacteristic
1054C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3804C2semidirect
2. C22×#3796C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63978C2semidirect
7. C2×#63971C2semidirect
8. C2×#63971C2semidirect
9. C2×#63910C2semidirect
10. C2×#63909C2semidirect
11. C2×#63899C2semidirect
12. C2×#63888C2semidirect
13. C2×#63886C2semidirect
14. C2×D3×Dic3⋊C4C2semidirect
15. C2×#63865C2semidirect
16. #10594059C2direct (N × H)
36. C2×#3804C22semidirect
41. C2×#3796C22semidirect
45. #64093C22semidirect
52. C3×#884C22semidirect
53. C3×#878C22semidirect
54. #63978C22semidirect
55. #63971C22semidirect
56. #63971C22semidirect
64. #63910C22semidirect
65. #63909C22semidirect
66. #63899C22semidirect
67. #63888C22semidirect
68. #63886C22semidirect
69. D3×Dic3⋊C4C22semidirect
70. #63865C22semidirect
101. C2×#884D3semidirect
103. C2×#878D3semidirect
154. C2×D3×Dic3D4semidirect
285. #884C2×D3semidirect
287. #878C2×D3semidirect
347. D3×Dic3C2×D4semidirect
756. C2×C32#537semidirect
923. C32C2×#537semidirect
993. C2×C3#5597semidirect
994. C2×C3#5629semidirect
1044. C3C2×#5597semidirect
1045. C3C2×#5629semidirect
1051. C2#10594059direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C22×#37962
C2×#640932
C2×C3×#8842
C2×C3×#8782
C2×#639782
C2×#639712
C2×#639102
C2×#639092
C2×#638992
C2×#638882
C2×#638862
C2×D3×Dic3⋊C42
C2×#638652
#105940592
C2×#56293
C2×#55973