Finite Group Databasebeta

← C2×#10594068 #11900790

Subgroups — C2×#10594068 #11900790

Order 1152.

3669 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×#3799C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#885C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63979C211yesmaximal, characteristic, complemented
7C2×#63958C211yesmaximal, characteristic, complemented
8C2×#63952C211yesmaximal, characteristic, complemented
9C2×#63912C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×C4×#624C211yesmaximal, characteristic, complemented
12C2×#63880C211yesmaximal, characteristic, complemented
13C2×#63879C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594068C2116yesmaximal, direct product factor
17C2×#5668—31nomaximal
18C2×#5548—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×C4×D3C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C22×#627C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#625C2211yescharacteristic
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×#624C2211yescharacteristic
37C2×#3804—28no—
38C2×#3804C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic
40C2×#3799—28no—
41C2×#3799C2218yescomplemented
42C2×C32×C22⋊C4C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3750C2211yescharacteristic
45#64093C2218yescomplemented
46C2×C3×#217C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×Dic3⋊C4C2211yescharacteristic
51C2×C3×C4×Dic3C2211yescharacteristic
52C2×C3×C4×Dic3C2211yescharacteristic
53C3×#885C2218yescomplemented
54C3×#67⋊C4C2218yescomplemented
55#63979C2218yescomplemented
56C2×#3724C2211yescharacteristic
57C2×Dic3⋊Dic3C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60#63958C2218yescomplemented
61C2×Dic32C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63#63952C2218yescomplemented
64#63912C2218yescomplemented
65#63910C2218yescomplemented
66C4×#624C2218yescomplemented
67#63880C2218yescomplemented
68#63879C2218yescomplemented
69#63852C2218yescomplemented
70#63839C2218yescomplemented
71C22×#239—31no—
72C22×#237—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#124—31no—
76C2×C3×C4×D4—31no—
77C2×#944—31no—
78C2×#940—31no—
79C2×#940—31no—
80C2×#938—31no—
81C2×C4×#67—31no—
82C2×C4×#67—31no—
83#5668—316no—
84#5548—316no—
85C2×#895—31no—
86C2×#888—31no—
87C2×#885—31no—
88C2×#885D311yescharacteristic, complemented
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—61no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#67⋊C4—31no—
99C2×#67⋊C4D311yescharacteristic, complemented
100C2×#875—31no—
101C2×C4×D12—31no—
102C2×C42×D3—31no—
103C2×C42×D3—31no—
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—24no—
113C2×#638C2314yes—
114C2×#638C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4⋊(C3⋊D3)—24no—
118C2×C4⋊(C3⋊D3)C2314yes—
119C2×C4×C3⋊D3—24no—
120C2×C4×C3⋊D3C2314yes—
121C2×C3×#67—24no—
122C2×C3×#67—24no—
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×C4×D3—24no—
134C2×C3×C4×D3C2314yes—
135C2×C3×Dic6—24no—
136C2×C3×Dic6C2314yes—
137C2×#627—24no—
138C2×#627C2314yes—
139C2×#626—24no—
140C2×#626—24no—
141C2×#626—24no—
142C2×#626—24no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#626C2314yes—
147C2×#625—24no—
148C2×#625C2314yes—
149C2×#624—24no—
150C2×#624—24no—
151C2×#624D418yescomplemented
152C2×#624C2314yes—
153C2×#624C2314yes—
154C2×#624C2314yes—
155#3804—232no—
156C2×D3×Dic3—24no—
157C2×D3×Dic3C2314yes—
158#3799—232no—
159C32×C22⋊C4C2314yes—
160#3752C2314yes—
161#3750C2314yes—
162C3×#217C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×Dic3⋊C4C2314yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2314yes—
169#3724C2314yes—
170Dic3⋊Dic3C2314yes—
171#3722C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173Dic32C2314yes—
174Dic32C2314yes—
175C2×#532—91noSylow
176C22×C3×Q8—31no—
177C22×C3×D4—31no—
178C22×C3×D4—31no—
179C23×C3×C4—31no—
180C23×C3×C4—31no—
181C22×#67—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—31no—
191C22×#67—61no—
192C22×#67—61no—
193C22×#67C2×D311yescharacteristic
194C22×#67C2×D311yescharacteristic
195C23×Dic3—31no—
196C23×Dic3C2×D311yescharacteristic
197C2×#239—38no—
198C2×#239—68no—
199C2×#237—38no—
200C2×#237—68no—
201C2×#235—38no—
202C2×#235—38no—
203C2×#235—68no—
204C2×#235—68no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—61no—
212C22×C4×D3—31no—
213C22×C4×D3—31no—
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×#124—38no—
227C3×C4×D4—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C22⋊C4—21no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4C2×D311yescharacteristic
235C2×C3×C22⋊C4C2×D311yescharacteristic
236C2×C3×C42—31no—
237C2×C3×C42—31no—
238C2×#217—31no—
239C2×#217C2×D311yescharacteristic
240#944—38no—
241#940—38no—
242#940—38no—
243#938—38no—
244C4×#67—38no—
245C4×#67—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—61no—
252C2×(C2×D3)⋊C4C2×D311yescharacteristic
253C2×(C2×D3)⋊C4C2×D311yescharacteristic
254C2×(C2×D3)⋊C4C2×D311yescharacteristic
255C2×C4⋊Dic3—31no—
256C2×Dic3⋊C4—31no—
257C2×Dic3⋊C4—31no—
258C2×Dic3⋊C4—31no—
259C2×Dic3⋊C4—31no—
260C2×Dic3⋊C4—31no—
261C2×Dic3⋊C4—61no—
262C2×Dic3⋊C4C2×D311yescharacteristic
263C2×C4×Dic3—31no—
264C2×C4×Dic3—31no—
265C2×C4×Dic3—31no—
266C2×C4×Dic3—31no—
267C2×C4×Dic3C2×D311yescharacteristic
268C2×C4×Dic3C2×D311yescharacteristic
269#895—38no—
270#888—38no—
271#885—38no—
272#885C2×D318yescomplemented
273#884—38no—
274#884—38no—
275#884—38no—
276#884—38no—
277#884—38no—
278#884—38no—
279#884—68no—
280#67⋊C4—38no—
281#67⋊C4—38no—
282#67⋊C4—38no—
283#67⋊C4C2×D318yescomplemented
284#875—38no—
285C4×D12—38no—
286C42×D3—38no—
287C42×D3—38no—
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⋊D3C2×D414yes—
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×D3—22no—
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—28no—
315C2×C3⋊Dic3—22no—
316C2×C3⋊Dic3#4114yescomplemented
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C4⋊(C3⋊D3)—28no—
320C4×C3⋊D3—28no—
321C3×#67—28no—
322C3×#67—28no—
323C2×C3×Dic3—22no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—28no—
327C2×C3×Dic3C2×D414yes—
328C2×C3×Dic3C2×D414yes—
329C2×C3×Dic3#4114yescomplemented
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C3×C4×D3—28no—
337C3×Dic6—28no—
338#627—28no—
339#626—28no—
340#626—28no—
341#626—28no—
342#626—28no—
343#625—28no—
344#624—28no—
345#624—28no—
346#624C2×D4116yescomplemented
347D3×Dic3—28no—
348C22×#41—91no—
349C22×#41—91no—
350#532—916no—
351C2×C4⋊Q8—91no—
352C2×#127—91no—
353C2×#124—31no—
354C2×#124—91no—
355C2×#121—91no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#121—91no—
359C2×C4×D4—31no—
360C2×C4×D4—91no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C22×C42—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—64no—
382C2×C3×D4—64no—
383C22×C3×C4—21no—
384C22×C3×C4—21no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—34no—
392C22×C3×C4—34no—
393C22×C3×C4—64no—
394C22×C3×C4—64no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C2×#67—24no—
400C2×#67—24no—
401C2×#67—34no—
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—34no—
411C2×#67—64no—
412C2×#67—64no—
413C2×#67—64no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—64no—
419C2×#67—64no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67—64no—
423C2×#67—124no—
424C2×#67—124no—
425C2×#67C22×D314yes—
426C2×#67C22×D314yes—
427C22×Dic3—24no—
428C22×Dic3—31no—
429C22×Dic3—31no—
430C22×Dic3—31no—
431C22×Dic3—31no—
432C22×Dic3—34no—
433C22×Dic3—61no—
434C22×Dic3—61no—
435C22×Dic3—64no—
436C22×Dic3C22×D314yes—
437C22×Dic3C22×D311yescharacteristic
438C22×Dic3C22×D311yescharacteristic
439C22×Dic3C22×D311yescharacteristic
440C22×Dic3C22×D311yescharacteristic
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443#239—632no—
444#237—632no—
445#235—632no—
446#235—632no—
447C2×D12—34no—
448C2×D12—34no—
449C2×D12—34no—
450C2×D12—34no—
451C2×D12—34no—
452C2×D12—34no—
453C2×D12—64no—
454C2×D12—64no—
455C2×D12—64no—
456C2×D12—64no—
457C2×D12—64no—
458C2×D12—64no—
459C2×D12—64no—
460C2×D12—124no—
461C2×C4×D3—24no—
462C2×C4×D3—38no—
463C2×C4×D3—38no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
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—64no—
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—64no—
481C2×C4×D3—124no—
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×C22⋊C4—24no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4—34no—
495C3×C22⋊C4C22×D314yes—
496C3×C22⋊C4C22×D314yes—
497C3×C42—34no—
498C3×C42—34no—
499#217—34no—
500#217C22×D314yes—
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—64no—
507(C2×D3)⋊C4C22×D314yes—
508(C2×D3)⋊C4C22×D314yes—
509(C2×D3)⋊C4C22×D314yes—
510C4⋊Dic3—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—64no—
517Dic3⋊C4C22×D314yes—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3C22×D314yes—
523C4×Dic3C22×D314yes—
524C22×C32—22no—
525C22×C32—22no—
526C22×C32—22no—
527C22×C32—44no—
528C22×C32C22×D412yes—
529C22×C32C2×#4112yes—
530C22×C32C2×#4112yes—
531C22×C32C2511yescharacteristic
532C2×C3⋊D3—28no—
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⋊D3C22×D414yes—
540C2×C3×D3—22no—
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×D3—44no—
548C32×C4—22no—
549C32×C4—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3C2×#4114yescomplemented
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D414yes—
556C3×Dic3C22×D414yes—
557C3×Dic3C2×#4114yescomplemented
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—91no—
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—
581C4⋊Q8—98no—
582#127—98no—
583#124—38no—
584#124—98no—
585#121—98no—
586#121—98no—
587#121—98no—
588#121—98no—
589C4×D4—38no—
590C4×D4—98no—
591C4×D4—98no—
592C4×D4—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C22⋊C4—31no—
598C2×C22⋊C4—31no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4—91no—
603C2×C22⋊C4—91no—
604C2×C22⋊C4D3211yescharacteristic
605C2×C42—31no—
606C2×C42—31no—
607C2×C42—98no—
608C2×C42—91no—
609C2×C42—91no—
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—32no—
619C23×C3—32no—
620C23×C3—42no—
621C23×C3—42no—
622C23×C3—42no—
623C23×C3—62no—
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—22no—
639C22×D3—34no—
640C22×D3—34no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—64no—
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—62no—
658C22×D3—122no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3C23×D312yes—
664C22×D3C23×D312yes—
665C3×Q8—68no—
666C3×D4—68no—
667C3×D4—68no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—34no—
675C2×C3×C4—34no—
676C2×C3×C4—34no—
677C2×C3×C4—32no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—32no—
681C2×C3×C4—32no—
682C2×C3×C4—32no—
683C2×C3×C4—42no—
684C2×C3×C4—42no—
685C2×C3×C4—68no—
686C2×C3×C4—68no—
687C2×C3×C4—62no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4C23×D312yes—
691C2×C3×C4C23×D312yes—
692C2×C3×C4C23×D312yes—
693C2×C3×C4C23×D312yes—
694#67—28no—
695#67—28no—
696#67—68no—
697#67—68no—
698#67—68no—
699#67—68no—
700#67—68no—
701#67—68no—
702#67—68no—
703#67—68no—
704#67—68no—
705#67—68no—
706#67—128no—
707#67—128no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—28no—
712C2×Dic3—34no—
713C2×Dic3—34no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—64no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—68no—
724C2×Dic3—122no—
725C2×Dic3#23514yescomplemented
726C2×Dic3D3×D414yes—
727C2×Dic3D3×D414yes—
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734D12—68no—
735D12—68no—
736D12—68no—
737D12—68no—
738D12—68no—
739D12—68no—
740D12—128no—
741C4×D3—28no—
742C4×D3—316no—
743C4×D3—316no—
744C4×D3—68no—
745C4×D3—68no—
746C4×D3—68no—
747C4×D3—68no—
748C4×D3—68no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—128no—
752Dic6—28no—
753Dic6—68no—
754Dic6—68no—
755C2×C32—42no—
756C2×C32#53214yescomplemented
757C2×C32C23×D411yescharacteristic
758C2×C32C22×#4111yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C3⋊D3—24no—
761C3⋊D3—42no—
762C3×D3—42no—
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—64no—
778C2×D4—64no—
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—184no—
788C2×D4—184no—
789C2×D4—184no—
790C2×D4—184no—
791C2×D4—184no—
792C2×D4—184no—
793C2×D4—184no—
794C2×D4—184no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—34no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—34no—
803C22×C4—64no—
804C22×C4—64no—
805C22×C4—94no—
806C22×C4—98no—
807C22×C4—94no—
808C22×C4—94no—
809C22×C4—94no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—94no—
813C22×C4—184no—
814C22×C4—184no—
815C22×C4—184no—
816C22×C4—184no—
817C22×C4C2×D3211yescharacteristic
818C22×C4C2×D3211yescharacteristic
819C4⋊C4—34no—
820C4⋊C4—94no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—34no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4C2×D3214yes—
831C42—34no—
832C42—34no—
833C42—94no—
834C42—94no—
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—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—44no—
849C22×C3—44no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—84no—
857C22×C3—124no—
858C22×C3—124no—
859C22×C3C2×#23512yes—
860C22×C3C2×D3×D412yes—
861C22×C3C2×D3×D412yes—
862C22×C3D3×#4112yes—
863C22×C3D3×#4112yes—
864C22×C3D3×#4112yes—
865C22×C3C24×D311yescharacteristic
866C22×C3C24×D311yescharacteristic
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—34no—
874C2×D3—34no—
875C2×D3—44no—
876C2×D3—44no—
877C2×D3—64no—
878C2×D3—68no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—68no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—122no—
891C2×D3—128no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—122no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3—244no—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—34no—
904C3×C4—34no—
905C3×C4—34no—
906C3×C4—42no—
907C3×C4—42no—
908C3×C4—62no—
909C3×C4—62no—
910C3×C4—62no—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—34no—
915Dic3—34no—
916Dic3—64no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3C2×#23514yescomplemented
921Dic3C2×D3×D414yes—
922Dic3C2×D3×D414yes—
923C32C2×#53211yescharacteristic, complemented, Sylow
924C23—22no—
925C23—22no—
926C23—22no—
927C23—32no—
928C23—32no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—94no—
936C23—92no—
937C23—92no—
938C23—182no—
939C23—182no—
940C23—182no—
941C23—182no—
942C23—182no—
943C23C22×D3212yes—
944C23C22×D3211yescharacteristic
945Q8—68no—
946Q8—188no—
947D4—68no—
948D4—68no—
949D4—188no—
950D4—188no—
951D4—188no—
952D4—188no—
953D4—188no—
954D4—188no—
955D4—188no—
956D4—188no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—34no—
960C2×C4—34no—
961C2×C4—34no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—32no—
966C2×C4—32no—
967C2×C4—32no—
968C2×C4—68no—
969C2×C4—68no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—916no—
974C2×C4—94no—
975C2×C4—92no—
976C2×C4—92no—
977C2×C4—188no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4—188no—
981C2×C4—182no—
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—82no—
991C2×C3—122no—
992C2×C3—122no—
993C2×C3#554814yescomplemented
994C2×C3#566814yescomplemented
995C2×C3C22×#23511yescharacteristic
996C2×C3C22×D3×D411yescharacteristic
997C2×C3C22×D3×D411yescharacteristic
998C2×C3C2×D3×#4111yescharacteristic
999C2×C3C2×D3×#4111yescharacteristic
1000C2×C3C2×D3×#4111yescharacteristic
1001D3—42no—
1002D3—42no—
1003D3—64no—
1004D3—64no—
1005D3—124no—
1006D3—122no—
1007D3—122no—
1008D3—242no—
1009C22—22no—
1010C22—22no—
1011C22—22no—
1012C22—44no—
1013C22—62no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—94no—
1020C22—124no—
1021C22—124no—
1022C22—188no—
1023C22—182no—
1024C22—182no—
1025C22—182no—
1026C22—182no—
1027C22—182no—
1028C22—364no—
1029C22D3×#23512yes—
1030C22D32×D412yes—
1031C22#6431212yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—22no—
1035C4—34no—
1036C4—34no—
1037C4—34no—
1038C4—62no—
1039C4—62no—
1040C4—62no—
1041C4—94no—
1042C4—182no—
1043C3—21no—
1044C3C2×#554811yescharacteristic, complemented
1045C3C2×#566811yescharacteristic, complemented
1046C2—42no—
1047C2—122no—
1048C2—122no—
1049C2—184no—
1050C2—362no—
1051C2#1059406814yesdirect product factor
1052C2C2×D3×#23511yescharacteristic
1053C2C2×D32×D411yescharacteristic
1054C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#532
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×#885C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63979C2semidirect
7. C2×#63958C2semidirect
8. C2×#63952C2semidirect
9. C2×#63912C2semidirect
10. C2×#63910C2semidirect
11. C2×C4×#624C2semidirect
12. C2×#63880C2semidirect
13. C2×#63879C2semidirect
14. C2×#63852C2semidirect
15. C2×#63839C2semidirect
16. #10594068C2direct (N × H)
38. C2×#3804C22semidirect
41. C2×#3799C22semidirect
45. #64093C22semidirect
53. C3×#885C22semidirect
54. C3×#67⋊C4C22semidirect
55. #63979C22semidirect
60. #63958C22semidirect
63. #63952C22semidirect
64. #63912C22semidirect
65. #63910C22semidirect
66. C4×#624C22semidirect
67. #63880C22semidirect
68. #63879C22semidirect
69. #63852C22semidirect
70. #63839C22semidirect
88. C2×#885D3semidirect
99. C2×#67⋊C4D3semidirect
151. C2×#624D4semidirect
272. #885C2×D3semidirect
283. #67⋊C4C2×D3semidirect
316. C2×C3⋊Dic3#41semidirect
329. C2×C3×Dic3#41semidirect
346. #624C2×D4semidirect
551. C3⋊Dic3C2×#41semidirect
557. C3×Dic3C2×#41semidirect
725. C2×Dic3#235semidirect
756. C2×C32#532semidirect
920. Dic3C2×#235semidirect
923. C32C2×#532semidirect
993. C2×C3#5548semidirect
994. C2×C3#5668semidirect
1044. C3C2×#5548semidirect
1045. C3C2×#5668semidirect
1051. C2#10594068direct (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×#8852
C2×C3×#67⋊C42
C2×#639792
C2×#639582
C2×#639522
C2×#639122
C2×#639102
C2×C4×#6242
C2×#638802
C2×#638792
C2×#638522
C2×#638392
#105940682
C2×#56683
C2×#55483