Finite Group Databasebeta

← C2×#10594147 #11903420

Subgroups — C2×#10594147 #11903420

Order 1152.

2385 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C211yesmaximal, characteristic
5C2×#63959C211yesmaximal, characteristic
6C2×#63957C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8C2×#63896C211yesmaximal, characteristic, complemented
9C2×#63877C211yesmaximal, characteristic, complemented
10C2×#63861C211yesmaximal, characteristic, complemented
11C2×#63858C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
14C2×#63839C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594147C2116yesmaximal, direct product factor
17C2×#5702—31nomaximal
18C2×#5671—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30#64087C2218yescomplemented
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#885C2218yes—
42C3×#879C2218yescomplemented
43#67⋊Dic3C2218yes—
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53#63959C2218yes—
54#63957C2218yescomplemented
55#63956C2218yescomplemented
56C2×Dic32C2211yescharacteristic
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63896C2218yescomplemented
62#63877C2218yescomplemented
63#63861C2218yescomplemented
64#63858C2218yescomplemented
65#63844C2218yescomplemented
66Dic3×Dic6C2218yescomplemented
67#63839C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#124—31no—
71C2×Q8×Dic3—31no—
72C2×#944—31no—
73C2×#936—31no—
74C2×D4×Dic3—31no—
75#5702—316no—
76#5671—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#896—31no—
80C2×#888—31no—
81C2×#887—31no—
82C2×#887—31no—
83C2×#885—31no—
84C2×#885D311yescharacteristic
85C2×#67⋊C4—31no—
86C2×#879—31no—
87C2×#879—31no—
88C2×#879—31no—
89C2×#879—31no—
90C2×#879D311yescharacteristic, complemented
91C2×#878—31no—
92C2×#878—31no—
93C2×#878—31no—
94C2×#878—61no—
95C2×#877—31no—
96C2×#877—31no—
97C2×#877—31no—
98C2×#872—31no—
99C2×C4×Dic6—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3—24no—
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2314yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—24no—
113C2×#634C2314yes—
114C2×C3×#67—24no—
115C2×C3×#67C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×Dic6—24no—
124C2×C3×Dic6C2314yes—
125C2×#627—24no—
126C2×#627C2314yes—
127C2×D3×Dic3—24no—
128C2×D3×Dic3C2314yes—
129C32×C22⋊C4C2314yes—
130#3757C2314yes—
131C4⋊(C3⋊Dic3)C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×#217C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150(C2×D3)⋊Dic3C2314yes—
151(C2×D3)⋊Dic3C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153Dic32C2314yes—
154Dic32C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#556—91noSylow
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×#67C2×D311yescharacteristic
162C23×Dic3—31no—
163C23×Dic3—31no—
164C23×Dic3—31no—
165C23×Dic3—61no—
166C22×C4×D3—31no—
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—61no—
172C22×Dic6C2×D311yescharacteristic
173C3×#126—38no—
174C3×#124—38no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—21no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C22⋊C4C2×D311yescharacteristic
186C2×C3×C42—31no—
187C2×C3×C42—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—61no—
194C2×#217C2×D311yescharacteristic
195C2×#217C2×D311yescharacteristic
196C2×#217C2×D311yescharacteristic
197Q8×Dic3—38no—
198#944—38no—
199#936—38no—
200D4×Dic3—38no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—61no—
212C2×C4⋊Dic3C2×D311yescharacteristic
213C2×Dic3⋊C4—31no—
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—61no—
227C2×Dic3⋊C4—61no—
228C2×Dic3⋊C4C2×D311yescharacteristic
229C2×Dic3⋊C4C2×D311yescharacteristic
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3C2×D311yescharacteristic
241C2×C4×Dic3C2×D311yescharacteristic
242#898—38no—
243#898—38no—
244#896—38no—
245#888—38no—
246#887—38no—
247#887—38no—
248#885—38no—
249#885C2×D318yes—
250#67⋊C4—38no—
251#879—38no—
252#879—38no—
253#879—38no—
254#879—38no—
255#879C2×D318yescomplemented
256#878—38no—
257#878—38no—
258#878—38no—
259#878—68no—
260#877—38no—
261#877—38no—
262#877—38no—
263#872—38no—
264C4×Dic6—38no—
265C4×Dic6—38no—
266C4×Dic6—38no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—22no—
270C23×C32C2412yes—
271C23×C32C2411yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4C2412yes—
279C2×C32×C4C2412yes—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—28no—
284C2×C3⋊Dic3#4114yes—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289#634—28no—
290C3×#67—28no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3#4114yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C3×Dic6—28no—
306#627—28no—
307D3×Dic3—28no—
308#556—916no—
309C2×C4⋊Q8—91no—
310C2×#126—31no—
311C2×#126—91no—
312C2×#126—91no—
313C2×#126—91no—
314C2×#124—31no—
315C2×#124—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×Q8—91no—
320C2×C4×Q8—91no—
321C2×C4×D4—91no—
322C2×#117—91no—
323C2×#117—91no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×Q8—34no—
330C2×C3×Q8—64no—
331C2×C3×D4—34no—
332C2×C3×D4—64no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
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—31no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C2×#67—24no—
347C2×#67C22×D314yes—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—34no—
351C22×Dic3—34no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—34no—
359C22×Dic3—61no—
360C22×Dic3—64no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—64no—
365C22×Dic3—64no—
366C22×Dic3—64no—
367C22×Dic3—124no—
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C2×C4×D3—34no—
376C2×C4×D3—64no—
377C2×Dic6—24no—
378C2×Dic6—34no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—34no—
382C2×Dic6—64no—
383C2×Dic6—64no—
384C2×Dic6—64no—
385C2×Dic6—64no—
386C2×Dic6—64no—
387C2×Dic6—124no—
388C2×Dic6C22×D314yes—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—34no—
398C3×C22⋊C4C22×D314yes—
399C3×C22⋊C4C22×D314yes—
400C3×C42—34no—
401C3×C42—34no—
402#217—34no—
403#217—34no—
404#217—34no—
405#217—34no—
406#217—34no—
407#217—64no—
408#217C22×D314yes—
409#217C22×D314yes—
410#217C22×D314yes—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4C22×D314yes—
415(C2×D3)⋊C4C22×D314yes—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—64no—
422C4⋊Dic3C22×D314yes—
423Dic3⋊C4—34no—
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—64no—
437Dic3⋊C4—64no—
438Dic3⋊C4C22×D314yes—
439Dic3⋊C4C22×D314yes—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3C22×D314yes—
451C4×Dic3C22×D314yes—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32—44no—
456C22×C32C2×#4112yes—
457C22×C32C2×#4112yes—
458C22×C322−1+412yes—
459C22×C32C2511yescharacteristic
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—44no—
464C32×C4—22no—
465C32×C4—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3C2×#4114yes—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3C2×#4114yes—
477C22×Q8—31no—
478C22×Q8—91no—
479C22×Q8—91no—
480C22×D4—31no—
481C23×C4—91no—
482C23×C4—91no—
483C4⋊Q8—98no—
484#126—38no—
485#126—98no—
486#126—98no—
487#126—98no—
488#124—38no—
489#124—98no—
490C22⋊Q8—98no—
491C22⋊Q8—98no—
492C4×Q8—98no—
493C4×Q8—98no—
494C4×Q8—98no—
495C4×D4—98no—
496#117—98no—
497#117—98no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4D3211yescharacteristic
520C2×C42—31no—
521C2×C42—31no—
522C2×C42—91no—
523C2×C42—91no—
524C2×C42—91no—
525C2×C42—91no—
526C2×C42—91no—
527C23×C3—24no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—21no—
536C23×C3—32no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3C23×D312yes—
543C23×C3C23×D312yes—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3C23×D312yes—
550C3×Q8—68no—
551C3×D4—68no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—34no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—42no—
567C2×C3×C4—42no—
568C2×C3×C4—62no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4C23×D312yes—
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D312yes—
578#67—28no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—34no—
586C2×Dic3—34no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—64no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—68no—
601C2×Dic3—68no—
602C2×Dic3—68no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—128no—
610C2×Dic3—122no—
611C2×Dic3—122no—
612C2×Dic3—122no—
613C2×Dic3#23714yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D312yes—
619C2×Dic3C23×D312yes—
620C2×Dic3C23×D312yes—
621C4×D3—68no—
622Dic6—28no—
623Dic6—68no—
624Dic6—68no—
625Dic6—68no—
626Dic6—68no—
627Dic6—128no—
628C2×C32—42no—
629C2×C32#55614yescomplemented
630C2×C32C22×#4111yescharacteristic
631C2×C32C22×#4111yescharacteristic
632C2×C32C2×2−1+411yescharacteristic
633C3×D3—42no—
634C24—31no—
635C24C2×D3211yescharacteristic
636C2×Q8—34no—
637C2×Q8—64no—
638C2×Q8—94no—
639C2×Q8—94no—
640C2×Q8—184no—
641C2×Q8—184no—
642C2×D4—34no—
643C2×D4—64no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—94no—
652C22×C4—91no—
653C22×C4—94no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—184no—
658C22×C4—184no—
659C22×C4C2×D3211yescharacteristic
660C22×C4C2×D3211yescharacteristic
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—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4—34no—
677C22⋊C4—34no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4C2×D3214yes—
683C42—34no—
684C42—34no—
685C42—94no—
686C42—94no—
687C42—94no—
688C42—94no—
689C42—94no—
690C22×C3—24no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—48no—
704C22×C3—44no—
705C22×C3—44no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—124no—
710C22×C3C2×#23712yes—
711C22×C3D3×#4112yes—
712C22×C3D3×#4112yes—
713C22×C3D3×#4112yes—
714C22×C3#101012yes—
715C22×C3#101012yes—
716C22×C3C24×D311yescharacteristic
717C22×C3C24×D311yescharacteristic
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—22no—
721C2×D3—44no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—34no—
727C3×C4—42no—
728C3×C4—42no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735Dic3—22no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—34no—
742Dic3—34no—
743Dic3—64no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—122no—
751Dic3—122no—
752Dic3—122no—
753Dic3C2×#23714yes—
754C32C2×#55611yescharacteristic, complemented, Sylow
755C23—22no—
756C23—22no—
757C23—22no—
758C23—32no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23C22×D3212yes—
763C23C22×D3211yescharacteristic
764Q8—68no—
765Q8—188no—
766Q8—188no—
767D4—68no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—34no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—94no—
785C2×C4—92no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—92no—
789C2×C4—188no—
790C2×C4—188no—
791C2×C4—182no—
792C2×C4—182no—
793C2×C4—182no—
794C2×C4C22×D3212yes—
795C2×C4C22×D3212yes—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—24no—
800C2×C3—44no—
801C2×C3—42no—
802C2×C3—42no—
803C2×C3—122no—
804C2×C3#567114yescomplemented
805C2×C3#570214yescomplemented
806C2×C3C22×#23711yescharacteristic
807C2×C3C2×D3×#4111yescharacteristic
808C2×C3C2×D3×#4111yescharacteristic
809C2×C3C2×D3×#4111yescharacteristic
810C2×C3C2×#101011yescharacteristic
811C2×C3C2×#101011yescharacteristic
812D3—42no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—44no—
817C22—62no—
818C22—62no—
819C22—62no—
820C22—124no—
821C22#6429812yes—
822C22D3×#23712yes—
823C22#6431212yes—
824C22C23×D3211yescharacteristic
825C4—22no—
826C4—22no—
827C4—34no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—62no—
834C4—94no—
835C4—182no—
836C4—182no—
837C4—182no—
838C3—21no—
839C3C2×#567111yescharacteristic, complemented
840C3C2×#570211yescharacteristic, complemented
841C2—42no—
842C2—122no—
843C2#1059414714yesdirect product factor
844C2C2×#6429811yescharacteristic
845C2C2×D3×#23711yescharacteristic
846C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#556
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×#64087C2semidirect
3. C2×C3×#879C2semidirect
6. C2×#63957C2semidirect
7. C2×#63956C2semidirect
8. C2×#63896C2semidirect
9. C2×#63877C2semidirect
10. C2×#63861C2semidirect
11. C2×#63858C2semidirect
12. C2×#63844C2semidirect
13. C2×Dic3×Dic6C2semidirect
14. C2×#63839C2semidirect
15. C2×#63837C2semidirect
16. #10594147C2direct (N × H)
30. #64087C22semidirect
42. C3×#879C22semidirect
54. #63957C22semidirect
55. #63956C22semidirect
61. #63896C22semidirect
62. #63877C22semidirect
63. #63861C22semidirect
64. #63858C22semidirect
65. #63844C22semidirect
66. Dic3×Dic6C22semidirect
67. #63839C22semidirect
68. #63837C22semidirect
90. C2×#879D3semidirect
255. #879C2×D3semidirect
629. C2×C32#556semidirect
754. C32C2×#556semidirect
804. C2×C3#5671semidirect
805. C2×C3#5702semidirect
839. C3C2×#5671semidirect
840. C3C2×#5702semidirect
843. C2#10594147direct (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×#8852
C2×C3×#8792
C2×#67⋊Dic32
C2×#639592
C2×#639572
C2×#639562
C2×#638962
C2×#638772
C2×#638612
C2×#638582
C2×#638442
C2×Dic3×Dic62
C2×#638392
C2×#638372
#105941472
C2×#57023
C2×#56713