Finite Group Databasebeta

← C2×#10594064 #11902550

Subgroups — C2×#10594064 #11902550

Order 1152.

3477 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#883C211yesmaximal, characteristic, complemented
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63975C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63952C211yesmaximal, characteristic, complemented
9C2×#63900C211yesmaximal, characteristic, complemented
10C2×#63897C211yesmaximal, characteristic, complemented
11C2×#63895C211yesmaximal, characteristic, complemented
12C2×#63890C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594064C2116yesmaximal, direct product factor
17C2×#5655—31nomaximal
18C2×#5631—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×#627C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C2×#3804—28no—
34C2×#3804C2218yescomplemented
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C2×#3799—28no—
38C2×#3799C2218yescomplemented
39C2×C32×C22⋊C4C2211yescharacteristic
40C2×#3752C2211yescharacteristic
41C2×#3750C2211yescharacteristic
42#64093C2218yescomplemented
43C2×C3×#217C2211yescharacteristic
44C2×C3×#217C2211yescharacteristic
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×C4⋊Dic3C2211yescharacteristic
47C2×C3×C4⋊Dic3C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic
49C2×C3×Dic3⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C3×#883C2218yescomplemented
52C3×#878C2218yescomplemented
53#63975C2218yescomplemented
54#63971C2218yescomplemented
55C2×#3724C2211yescharacteristic
56C2×#3724C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58C2×Dic3⋊Dic3C2211yescharacteristic
59C2×#3722C2211yescharacteristic
60C2×#3722C2211yescharacteristic
61C2×#3722C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63#63952C2218yescomplemented
64#63900C2218yescomplemented
65#63897C2218yescomplemented
66#63895C2218yescomplemented
67#63890C2218yescomplemented
68#63881C2218yescomplemented
69D3×Dic3⋊C4C2218yescomplemented
70#63839C2218yescomplemented
71C22×#239—31no—
72C22×#237—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×C22⋊Q8—31no—
77C2×#944—31no—
78C2×#939—31no—
79C2×C4×#67—31no—
80C22×Dic3⋊C4—31no—
81#5655—316no—
82#5631—316no—
83C2×#897—31no—
84C2×#896—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#893—31no—
89C2×D3×C4⋊C4—31no—
90C2×D3×C4⋊C4—31no—
91C2×D3×C4⋊C4—31no—
92C2×#888—31no—
93C2×#886—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#884—61no—
98C2×#883—31no—
99C2×#883—31no—
100C2×#883D311yescharacteristic, complemented
101C2×#67⋊C4—31no—
102C2×#67⋊C4—31no—
103C2×#878D311yescharacteristic, complemented
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×#638—24no—
111C2×#638—24no—
112C2×#638C2314yes—
113C2×#638C2314yes—
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4⋊(C3⋊D3)—24no—
117C2×C4⋊(C3⋊D3)C2314yes—
118C2×C4×C3⋊D3—24no—
119C2×C4×C3⋊D3C2314yes—
120C2×C3×#67—24no—
121C2×C3×#67C2314yes—
122C22×C3×Dic3—24no—
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3C2314yes—
133C2×C3×Dic6—24no—
134C2×C3×Dic6C2314yes—
135C2×#627—24no—
136C2×#627C2314yes—
137C2×#626—24no—
138C2×#626D418yescomplemented
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—24no—
142C2×#624—24no—
143C2×#624—24no—
144C2×#624C2314yes—
145C2×#624C2314yes—
146C2×#624C2314yes—
147#3804—232no—
148C2×D3×Dic3—24no—
149C2×D3×Dic3—24no—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152#3799—232no—
153C32×C22⋊C4C2314yes—
154#3752C2314yes—
155#3750C2314yes—
156C3×#217C2314yes—
157C3×#217C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×C4⋊Dic3C2314yes—
160C3×C4⋊Dic3C2314yes—
161C3×Dic3⋊C4C2314yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164#3724C2314yes—
165#3724C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168#3722C2314yes—
169#3722C2314yes—
170#3722C2314yes—
171Dic32C2314yes—
172C2×#547—91noSylow
173C22×C3×Q8—31no—
174C22×C3×D4—31no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—61no—
184C22×#67—61no—
185C22×#67C2×D311yescharacteristic
186C23×Dic3—31no—
187C23×Dic3—31no—
188C23×Dic3C2×D311yescharacteristic
189C2×#239—38no—
190C2×#239—68no—
191C2×#237—38no—
192C2×#237—68no—
193C2×#235—38no—
194C2×#235—38no—
195C2×#235—68no—
196C2×#235—68no—
197C22×D12—31no—
198C22×D12—31no—
199C22×D12—31no—
200C22×D12—31no—
201C22×D12—61no—
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—61no—
213C22×C4×D3C2×D311yescharacteristic
214C22×Dic6—31no—
215C22×Dic6—31no—
216C22×Dic6C2×D311yescharacteristic
217C3×#123—38no—
218C3×C22⋊Q8—38no—
219C2×C3×C4⋊C4—31no—
220C2×C3×C4⋊C4—31no—
221C2×C3×C4⋊C4—31no—
222C2×C3×C4⋊C4—31no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C22⋊C4—21no—
225C2×C3×C22⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4C2×D311yescharacteristic
229C2×C3×C22⋊C4C2×D311yescharacteristic
230C2×#217C2×D311yescharacteristic
231C2×#217C2×D311yescharacteristic
232#944—38no—
233#939—38no—
234C4×#67—38no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—61no—
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3C2×D311yescharacteristic
248C2×C4⋊Dic3C2×D311yescharacteristic
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4—31no—
255C2×Dic3⋊C4—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—38no—
258C2×Dic3⋊C4—61no—
259C2×Dic3⋊C4C2×D311yescharacteristic
260C2×Dic3⋊C4C2×D311yescharacteristic
261C2×Dic3⋊C4C2×D311yescharacteristic
262C2×C4×Dic3—31no—
263C2×C4×Dic3—31no—
264#897—38no—
265#896—38no—
266#894—38no—
267#894—38no—
268#894—38no—
269#893—38no—
270D3×C4⋊C4—38no—
271D3×C4⋊C4—38no—
272D3×C4⋊C4—38no—
273#888—38no—
274#886—38no—
275#884—38no—
276#884—38no—
277#884—38no—
278#884—68no—
279#883—38no—
280#883—38no—
281#883C2×D318yescomplemented
282#67⋊C4—38no—
283#67⋊C4—38no—
284#878C2×D318yescomplemented
285C23×C32—22no—
286C23×C32—22no—
287C23×C32—22no—
288C23×C32C2412yes—
289C23×C32C2411yescharacteristic
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3C2×D414yes—
296C22×C3⋊D3C2412yes—
297C22×C3⋊D3C2412yes—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2×D414yes—
301C22×C3×D3C2412yes—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306#638—28no—
307#638—28no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3#4114yescomplemented
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C4⋊(C3⋊D3)—28no—
313C4×C3⋊D3—28no—
314C3×#67—28no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—28no—
322C2×C3×Dic3C2×D414yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2412yes—
330C3×C4×D3—28no—
331C3×Dic6—28no—
332#627—28no—
333#626—28no—
334#626C2×D4116yescomplemented
335#624—28no—
336#624—28no—
337#624—28no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340C22×#41—91no—
341C22×#41—91no—
342#547—916no—
343C2×C4⋊Q8—91no—
344C2×#123—31no—
345C2×#123—91no—
346C2×#123—91no—
347C2×#123—91no—
348C2×C22⋊Q8—31no—
349C2×C22⋊Q8—91no—
350C2×#121—91no—
351C2×#121—91no—
352C2×C4×D4—91no—
353C2×C4×D4—91no—
354C22×C4⋊C4—91no—
355C22×C4⋊C4—91no—
356C24×C3—21no—
357C24×C3—31no—
358C24×C3C22×D311yescharacteristic
359C24×C3C22×D311yescharacteristic
360C23×D3—31no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—61no—
365C23×D3—61no—
366C23×D3C22×D311yescharacteristic
367C2×C3×Q8—34no—
368C2×C3×Q8—64no—
369C2×C3×D4—34no—
370C2×C3×D4—64no—
371C22×C3×C4—21no—
372C22×C3×C4—21no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—64no—
383C22×C3×C4—64no—
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C2×#67—24no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—38no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—64no—
397C2×#67—64no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—64no—
403C2×#67—124no—
404C2×#67—124no—
405C2×#67C22×D314yes—
406C22×Dic3—24no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—34no—
412C22×Dic3—34no—
413C22×Dic3—61no—
414C22×Dic3—61no—
415C22×Dic3—64no—
416C22×Dic3—64no—
417C22×Dic3C22×D314yes—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425#239—632no—
426#237—632no—
427#235—632no—
428#235—632no—
429C2×D12—38no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—64no—
435C2×D12—64no—
436C2×D12—64no—
437C2×D12—64no—
438C2×D12—124no—
439C2×C4×D3—24no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—34no—
446C2×C4×D3—34no—
447C2×C4×D3—34no—
448C2×C4×D3—34no—
449C2×C4×D3—34no—
450C2×C4×D3—64no—
451C2×C4×D3—64no—
452C2×C4×D3—64no—
453C2×C4×D3—64no—
454C2×C4×D3—64no—
455C2×C4×D3—64no—
456C2×C4×D3—64no—
457C2×C4×D3—64no—
458C2×C4×D3—64no—
459C2×C4×D3—64no—
460C2×C4×D3—64no—
461C2×C4×D3—124no—
462C2×C4×D3C22×D314yes—
463C2×Dic6—24no—
464C2×Dic6—34no—
465C2×Dic6—34no—
466C2×Dic6—64no—
467C2×Dic6—64no—
468C2×Dic6C22×D314yes—
469C3×C4⋊C4—34no—
470C3×C4⋊C4—34no—
471C3×C4⋊C4—34no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—34no—
474C3×C22⋊C4—24no—
475C3×C22⋊C4—34no—
476C3×C22⋊C4—34no—
477C3×C22⋊C4—34no—
478C3×C22⋊C4C22×D314yes—
479C3×C22⋊C4C22×D314yes—
480#217C22×D314yes—
481#217C22×D314yes—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—64no—
491(C2×D3)⋊C4C22×D314yes—
492C4⋊Dic3—34no—
493C4⋊Dic3—34no—
494C4⋊Dic3C22×D314yes—
495C4⋊Dic3C22×D314yes—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—34no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—64no—
505Dic3⋊C4C22×D314yes—
506Dic3⋊C4C22×D314yes—
507Dic3⋊C4C22×D314yes—
508C4×Dic3—34no—
509C4×Dic3—34no—
510C22×C32—22no—
511C22×C32—22no—
512C22×C32—22no—
513C22×C32—44no—
514C22×C32C22×D412yes—
515C22×C32C2×#4112yes—
516C22×C322−1+412yes—
517C22×C32C2511yescharacteristic
518C2×C3⋊D3—28no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—44no—
525C2×C3⋊D3C22×D414yes—
526C2×C3×D3—28no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3C22×D414yes—
530C32×C4—22no—
531C32×C4—22no—
532C3⋊Dic3—22no—
533C3⋊Dic3C2×#4114yescomplemented
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—22no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3C22×D414yes—
541C2×#41—98no—
542C2×#41—98no—
543C2×#41—188no—
544C2×#41—188no—
545C22×Q8—31no—
546C22×Q8—91no—
547C22×D4—31no—
548C22×D4—91no—
549C22×D4—91no—
550C22×D4—91no—
551C22×D4—91no—
552C22×D4—91no—
553C23×C4—31no—
554C23×C4—31no—
555C23×C4—91no—
556C23×C4—91no—
557C23×C4—91no—
558C23×C4—91no—
559C23×C4—91no—
560C23×C4—91no—
561C4⋊Q8—98no—
562#123—38no—
563#123—98no—
564#123—98no—
565#123—98no—
566C22⋊Q8—38no—
567C22⋊Q8—98no—
568#121—98no—
569#121—98no—
570C4×D4—98no—
571C4×D4—98no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—31no—
574C2×C4⋊C4—31no—
575C2×C4⋊C4—31no—
576C2×C4⋊C4—31no—
577C2×C4⋊C4—98no—
578C2×C4⋊C4—98no—
579C2×C4⋊C4—91no—
580C2×C4⋊C4—91no—
581C2×C4⋊C4—91no—
582C2×C4⋊C4—91no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—31no—
585C2×C22⋊C4—31no—
586C2×C22⋊C4—31no—
587C2×C22⋊C4—91no—
588C2×C22⋊C4—91no—
589C2×C22⋊C4—91no—
590C2×C22⋊C4—91no—
591C2×C22⋊C4D3211yescharacteristic
592C2×C42—91no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—21no—
601C23×C3—34no—
602C23×C3—32no—
603C23×C3—42no—
604C23×C3—42no—
605C23×C3—42no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3C23×D312yes—
609C23×C3C23×D312yes—
610C23×C3C23×D311yescharacteristic
611C23×C3C23×D311yescharacteristic
612C22×D3—22no—
613C22×D3—22no—
614C22×D3—34no—
615C22×D3—34no—
616C22×D3—32no—
617C22×D3—32no—
618C22×D3—32no—
619C22×D3—32no—
620C22×D3—64no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—122no—
637C22×D3—122no—
638C22×D3D3×D414yes—
639C22×D3C23×D312yes—
640C3×Q8—68no—
641C3×D4—68no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—34no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—32no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—42no—
657C2×C3×C4—42no—
658C2×C3×C4—68no—
659C2×C3×C4—68no—
660C2×C3×C4—62no—
661C2×C3×C4—62no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4C23×D312yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669C2×C3×C4C23×D312yes—
670#67—28no—
671#67—316no—
672#67—68no—
673#67—68no—
674#67—68no—
675#67—68no—
676#67—68no—
677#67—128no—
678#67—128no—
679C2×Dic3—22no—
680C2×Dic3—22no—
681C2×Dic3—22no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—28no—
686C2×Dic3—34no—
687C2×Dic3—34no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—64no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—68no—
696C2×Dic3—68no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—122no—
700C2×Dic3D3×D414yes—
701C2×Dic3C23×D312yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708D12—316no—
709D12—68no—
710D12—68no—
711D12—68no—
712D12—128no—
713C4×D3—28no—
714C4×D3—68no—
715C4×D3—68no—
716C4×D3—68no—
717C4×D3—68no—
718C4×D3—68no—
719C4×D3—68no—
720C4×D3—68no—
721C4×D3—68no—
722C4×D3—68no—
723C4×D3—68no—
724C4×D3—128no—
725Dic6—28no—
726Dic6—68no—
727Dic6—68no—
728C2×C32—42no—
729C2×C32#54714yescomplemented
730C2×C32C23×D411yescharacteristic
731C2×C32C22×#4111yescharacteristic
732C2×C32C2×2−1+411yescharacteristic
733C3⋊D3—24no—
734C3⋊D3—42no—
735C3×D3—24no—
736C24—31no—
737C24—91no—
738C24—91no—
739C24C2×D3211yescharacteristic
740#41—1832no—
741#41—1832no—
742C2×Q8—34no—
743C2×Q8—64no—
744C2×Q8—94no—
745C2×Q8—184no—
746C2×D4—34no—
747C2×D4—64no—
748C2×D4—94no—
749C2×D4—98no—
750C2×D4—94no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—184no—
755C2×D4—184no—
756C2×D4—184no—
757C2×D4—184no—
758C22×C4—31no—
759C22×C4—34no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—34no—
767C22×C4—64no—
768C22×C4—64no—
769C22×C4—94no—
770C22×C4—94no—
771C22×C4—94no—
772C22×C4—94no—
773C22×C4—94no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—94no—
777C22×C4—184no—
778C22×C4—184no—
779C22×C4—184no—
780C22×C4—184no—
781C22×C4—184no—
782C22×C4—184no—
783C22×C4C2×D3211yescharacteristic
784C22×C4C2×D3211yescharacteristic
785C4⋊C4—34no—
786C4⋊C4—34no—
787C4⋊C4—34no—
788C4⋊C4—34no—
789C4⋊C4—34no—
790C4⋊C4—94no—
791C4⋊C4—94no—
792C4⋊C4—94no—
793C4⋊C4—94no—
794C4⋊C4—94no—
795C22⋊C4—34no—
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—94no—
799C22⋊C4—94no—
800C22⋊C4—94no—
801C22⋊C4—94no—
802C22⋊C4C2×D3214yes—
803C42—94no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—21no—
814C22×C3—34no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—44no—
819C22×C3—44no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—68no—
823C22×C3—84no—
824C22×C3C2×D3×D412yes—
825C22×C3C2×D3×D412yes—
826C22×C3#100712yes—
827C22×C3D3×#4112yes—
828C22×C3D3×#4112yes—
829C22×C3#101012yes—
830C22×C3C24×D311yescharacteristic
831C22×C3C24×D311yescharacteristic
832C2×D3—28no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—34no—
836C2×D3—34no—
837C2×D3—64no—
838C2×D3—68no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—68no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—122no—
851C2×D3—128no—
852C2×D3—122no—
853C2×D3—122no—
854C2×D3—122no—
855C2×D3—122no—
856C2×D3—124no—
857C2×D3—124no—
858C2×D3—244no—
859C2×D3C2×D3×D414yes—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—34no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—22no—
878Dic3—22no—
879Dic3—34no—
880Dic3—34no—
881Dic3—64no—
882Dic3—62no—
883Dic3—62no—
884Dic3—122no—
885Dic3C2×D3×D414yes—
886C32C2×#54711yescharacteristic, complemented, Sylow
887C23—22no—
888C23—22no—
889C23—22no—
890C23—34no—
891C23—32no—
892C23—62no—
893C23—62no—
894C23—94no—
895C23—92no—
896C23—92no—
897C23—182no—
898C23—182no—
899C23—182no—
900C23—182no—
901C23—182no—
902C23C22×D3212yes—
903C23C22×D3211yescharacteristic
904Q8—68no—
905Q8—188no—
906D4—68no—
907D4—916no—
908D4—188no—
909D4—188no—
910D4—188no—
911D4—188no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—34no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—32no—
922C2×C4—68no—
923C2×C4—68no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—94no—
931C2×C4—92no—
932C2×C4—92no—
933C2×C4—188no—
934C2×C4—188no—
935C2×C4—188no—
936C2×C4—188no—
937C2×C4—188no—
938C2×C4—188no—
939C2×C4—182no—
940C2×C4C22×D3212yes—
941C2×C4C22×D3212yes—
942C2×C3—24no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—42no—
947C2×C3—42no—
948C2×C3—64no—
949C2×C3—82no—
950C2×C3#563114yescomplemented
951C2×C3#565514yescomplemented
952C2×C3C22×D3×D411yescharacteristic
953C2×C3C22×D3×D411yescharacteristic
954C2×C3C2×#100711yescharacteristic
955C2×C3C2×D3×#4111yescharacteristic
956C2×C3C2×D3×#4111yescharacteristic
957C2×C3C2×#101011yescharacteristic
958D3—24no—
959D3—64no—
960D3—64no—
961D3—124no—
962D3—122no—
963D3—122no—
964D3—242no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—34no—
969C22—44no—
970C22—68no—
971C22—62no—
972C22—62no—
973C22—94no—
974C22—188no—
975C22—182no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—182no—
980C22—364no—
981C22#6429712yes—
982C22D32×D412yes—
983C22#6431212yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—22no—
987C4—34no—
988C4—62no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—62no—
993C4—62no—
994C4—94no—
995C4—182no—
996C3—21no—
997C3C2×#563111yescharacteristic, complemented
998C3C2×#565511yescharacteristic, complemented
999C2—42no—
1000C2—64no—
1001C2—184no—
1002C2—362no—
1003C2#1059406414yesdirect product factor
1004C2C2×#6429711yescharacteristic
1005C2C2×D32×D411yescharacteristic
1006C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#547
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×#3799C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#883C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63975C2semidirect
7. C2×#63971C2semidirect
8. C2×#63952C2semidirect
9. C2×#63900C2semidirect
10. C2×#63897C2semidirect
11. C2×#63895C2semidirect
12. C2×#63890C2semidirect
13. C2×#63881C2semidirect
14. C2×D3×Dic3⋊C4C2semidirect
15. C2×#63839C2semidirect
16. #10594064C2direct (N × H)
34. C2×#3804C22semidirect
38. C2×#3799C22semidirect
42. #64093C22semidirect
51. C3×#883C22semidirect
52. C3×#878C22semidirect
53. #63975C22semidirect
54. #63971C22semidirect
63. #63952C22semidirect
64. #63900C22semidirect
65. #63897C22semidirect
66. #63895C22semidirect
67. #63890C22semidirect
68. #63881C22semidirect
69. D3×Dic3⋊C4C22semidirect
70. #63839C22semidirect
100. C2×#883D3semidirect
103. C2×#878D3semidirect
138. C2×#626D4semidirect
281. #883C2×D3semidirect
284. #878C2×D3semidirect
309. C2×C3⋊Dic3#41semidirect
334. #626C2×D4semidirect
533. C3⋊Dic3C2×#41semidirect
729. C2×C32#547semidirect
886. C32C2×#547semidirect
950. C2×C3#5631semidirect
951. C2×C3#5655semidirect
997. C3C2×#5631semidirect
998. C3C2×#5655semidirect
1003. C2#10594064direct (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×#37992
C2×#640932
C2×C3×#8832
C2×C3×#8782
C2×#639752
C2×#639712
C2×#639522
C2×#639002
C2×#638972
C2×#638952
C2×#638902
C2×#638812
C2×D3×Dic3⋊C42
C2×#638392
#105940642
C2×#56553
C2×#56313