Finite Group Databasebeta

← C2×#10595202 #11900626

Subgroups — C2×#10595202 #11900626

Order 1152.

2677 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#939C211yesmaximal, characteristic
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63964C211yesmaximal, characteristic, complemented
7C2×#63961C211yesmaximal, characteristic, complemented
8C2×#63959C211yesmaximal, characteristic, complemented
9C2×#63957C211yesmaximal, characteristic, complemented
10C2×#63956C211yesmaximal, characteristic, complemented
11C22×Dic32C211yesmaximal, characteristic, complemented
12#10595202C2116yesmaximal, direct product factor
13C2×#63878C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63845C211yesmaximal, characteristic, complemented
16C2×#63838C211yesmaximal, characteristic, complemented
17C2×#5649—31nomaximal
18C2×#5600—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30D4×C3⋊Dic3C2218yescomplemented
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×#939C2218yes—
38C3×#935C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43#67⋊Dic3C2218yescomplemented
44#67⋊Dic3C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51#63964C2218yescomplemented
52#63961C2218yescomplemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56#63959C2218yescomplemented
57#63957C2218yescomplemented
58#63956C2218yescomplemented
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61C2×Dic32C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64C2×Dic32C2218yescomplemented
65#63878C2218yescomplemented
66#63861C2218yescomplemented
67#63845C2218yescomplemented
68#63838C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#939D311yescharacteristic
72C2×#936—31no—
73C2×#935—31no—
74C2×#935D311yescharacteristic, complemented
75C2×D4×Dic3—31no—
76C2×D4×Dic3—31no—
77C2×D4×Dic3—31no—
78C2×D4×Dic3—31no—
79C2×D4×Dic3—61no—
80C2×#929—31no—
81C2×#924—31no—
82C22×C4×Dic3—31no—
83C22×C4×Dic3—31no—
84#5649—316no—
85#5600—316no—
86C2×#898—31no—
87C2×#892—31no—
88C2×#890—31no—
89C2×#889—31no—
90C2×#887—31no—
91C2×#887—31no—
92C2×#885—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#879—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#877—31no—
101C2×#877—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C2×C32×D4—24no—
106C2×C32×D4C2314yes—
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3—24no—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2314yes—
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C3×#67—24no—
117C2×C3×#67—24no—
118C2×C3×#67C2314yes—
119C2×C3×#67C2314yes—
120C22×C3×Dic3—24no—
121C22×C3×Dic3—24no—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C2×#627—24no—
132C2×#627C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3C2314yes—
135#3757C2314yes—
136#3757C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138C4×C3⋊Dic3C2314yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#529—91noSylow
162C22×C3×D4—21no—
163C22×C3×D4—31no—
164C22×C3×D4—31no—
165C22×C3×D4C2×D311yescharacteristic
166C22×C3×D4C2×D311yescharacteristic
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C22×#67C2×D311yescharacteristic
170C22×#67C2×D311yescharacteristic
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C23×Dic3—31no—
176C23×Dic3—61no—
177C23×Dic3—61no—
178C23×Dic3C2×D311yescharacteristic
179C23×Dic3C2×D311yescharacteristic
180C22×C4×D3—31no—
181C22×Dic6—31no—
182C22×Dic6—31no—
183C3×#123—38no—
184C3×#121—38no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—61no—
201C2×#217—61no—
202C2×#217C2×D311yescharacteristic
203C2×#217C2×D311yescharacteristic
204C2×#217C2×D311yescharacteristic
205C2×#217C2×D311yescharacteristic
206#939C2×D318yes—
207#936—38no—
208#935—38no—
209#935C2×D318yescomplemented
210D4×Dic3—38no—
211D4×Dic3—38no—
212D4×Dic3—38no—
213D4×Dic3—38no—
214D4×Dic3—68no—
215#929—38no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3—61no—
226#924—38no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—38no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—38no—
253C2×C4×Dic3—61no—
254#898—38no—
255#892—38no—
256#890—38no—
257#889—38no—
258#887—38no—
259#887—38no—
260#885—38no—
261#67⋊C4—38no—
262#67⋊C4—38no—
263#879—38no—
264#879—38no—
265#879—38no—
266#878—38no—
267#877—38no—
268#877—38no—
269#877—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C32×D4—28no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—28no—
290C2×C3⋊Dic3—28no—
291C2×C3⋊Dic3#4114yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296C3×#67—28no—
297C3×#67—28no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—28no—
306C2×C3×Dic3#4114yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314#627—28no—
315D3×Dic3—28no—
316#529—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#124—91no—
321C2×#123—31no—
322C2×#123—91no—
323C2×C22⋊Q8—91no—
324C2×#121—31no—
325C2×C4×Q8—91no—
326C2×C4×D4—91no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×#117—91no—
330C2×#117—91no—
331C22×C42—91no—
332C24×C3—21no—
333C24×C3—21no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C24×C3C22×D311yescharacteristic
338C24×C3C22×D311yescharacteristic
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—28no—
341C2×C3×D4—24no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—34no—
345C2×C3×D4—34no—
346C2×C3×D4—64no—
347C2×C3×D4—64no—
348C2×C3×D4C22×D314yes—
349C2×C3×D4C22×D314yes—
350C22×C3×C4—21no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—34no—
356C22×C3×C4—34no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—64no—
361C22×C3×C4—64no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—24no—
365C2×#67—24no—
366C2×#67C22×D314yes—
367C2×#67C22×D314yes—
368C22×Dic3—24no—
369C22×Dic3—24no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—34no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—34no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—34no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—64no—
388C22×Dic3—64no—
389C22×Dic3—64no—
390C22×Dic3—64no—
391C22×Dic3—64no—
392C22×Dic3—64no—
393C22×Dic3—64no—
394C22×Dic3—124no—
395C22×Dic3—124no—
396C22×Dic3C22×D314yes—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D314yes—
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×C4×D3—34no—
406C2×C4×D3—64no—
407C2×Dic6—34no—
408C2×Dic6—34no—
409C2×Dic6—64no—
410C2×Dic6—64no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—34no—
426#217—64no—
427#217—64no—
428#217C22×D314yes—
429#217C22×D314yes—
430#217C22×D314yes—
431#217C22×D314yes—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4C22×D314yes—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—64no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4C22×D314yes—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D314yes—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—64no—
467C22×C32—22no—
468C22×C32—28no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—44no—
474C22×C32C2×#4114yes—
475C22×C32C2×#4112yes—
476C22×C32C2×#4112yes—
477C22×C32C2×#4112yes—
478C22×C32C2511yescharacteristic
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—44no—
483C32×C4—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3C2×#4114yes—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3C2×#4114yes—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4D3211yescharacteristic
499C23×C4—31no—
500C23×C4—31no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504#126—98no—
505#126—98no—
506#125—98no—
507#124—98no—
508#123—38no—
509#123—98no—
510C22⋊Q8—98no—
511#121—38no—
512C4×Q8—98no—
513C4×D4—98no—
514C4×D4—98no—
515C4×D4—98no—
516#117—98no—
517#117—98no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C42—91no—
539C2×C42—91no—
540C2×C42—91no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—98no—
544C2×C42—91no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—24no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—21no—
559C23×C3—24no—
560C23×C3—32no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3#23714yes—
569C23×C3#23714yes—
570C23×C3C23×D312yes—
571C23×C3C23×D312yes—
572C23×C3C23×D312yes—
573C23×C3C23×D312yes—
574C23×C3C23×D311yescharacteristic
575C23×C3C23×D311yescharacteristic
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3C23×D312yes—
580C3×D4—216no—
581C3×D4—28no—
582C3×D4—28no—
583C3×D4—68no—
584C3×D4—68no—
585C2×C3×C4—24no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—34no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—68no—
598C2×C3×C4—62no—
599C2×C3×C4—68no—
600C2×C3×C4—62no—
601C2×C3×C4—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607#67—28no—
608#67—28no—
609C2×Dic3—22no—
610C2×Dic3—28no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—28no—
617C2×Dic3—34no—
618C2×Dic3—34no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—64no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—68no—
633C2×Dic3—68no—
634C2×Dic3—68no—
635C2×Dic3—68no—
636C2×Dic3—68no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—128no—
644C2×Dic3—128no—
645C2×Dic3—122no—
646C2×Dic3—122no—
647C2×Dic3—122no—
648C2×Dic3#23714yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652C2×Dic3C23×D312yes—
653C2×Dic3C23×D312yes—
654C2×Dic3C23×D312yes—
655C2×Dic3C23×D312yes—
656C4×D3—68no—
657Dic6—68no—
658Dic6—68no—
659C2×C32—24no—
660C2×C32—42no—
661C2×C32#52914yescomplemented
662C2×C32C22×#4111yescharacteristic
663C2×C32C22×#4111yescharacteristic
664C2×C32C22×#4111yescharacteristic
665C3×D3—42no—
666C24—31no—
667C24C2×D3211yescharacteristic
668C24C2×D3211yescharacteristic
669C2×Q8—94no—
670C2×Q8—184no—
671C2×D4—24no—
672C2×D4—34no—
673C2×D4—34no—
674C2×D4—64no—
675C2×D4—64no—
676C2×D4C2×D3214yes—
677C22×C4—31no—
678C22×C4—34no—
679C22×C4—34no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—64no—
687C22×C4—64no—
688C22×C4—94no—
689C22×C4—91no—
690C22×C4—94no—
691C22×C4—94no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—184no—
696C22×C4—184no—
697C22×C4—184no—
698C22×C4C2×D3211yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C42—94no—
720C42—94no—
721C42—94no—
722C42—94no—
723C42—94no—
724C42—94no—
725C22×C3—28no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—28no—
731C22×C3—24no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—24no—
742C22×C3—21no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—48no—
747C22×C3—42no—
748C22×C3—48no—
749C22×C3—44no—
750C22×C3—44no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—124no—
755C22×C3C2×#23712yes—
756C22×C3C2×#23714yes—
757C22×C3C2×#23714yes—
758C22×C3C2×#23712yes—
759C22×C3C2×#23712yes—
760C22×C3D3×#4112yes—
761C22×C3D3×#4112yes—
762C22×C3D3×#4112yes—
763C22×C3C24×D311yescharacteristic
764C22×C3C24×D311yescharacteristic
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—44no—
769C3×C4—24no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—34no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779Dic3—22no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—34no—
786Dic3—34no—
787Dic3—64no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—62no—
794Dic3—122no—
795Dic3—122no—
796Dic3—122no—
797Dic3C2×#23714yes—
798C32C2×#52911yescharacteristic, complemented, Sylow
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—32no—
805C23—62no—
806C23—62no—
807C23—62no—
808C23#380514yes—
809C23C22×D3212yes—
810C23C22×D3212yes—
811C23C22×D3211yescharacteristic
812Q8—188no—
813D4—28no—
814D4—68no—
815D4—68no—
816C2×C4—22no—
817C2×C4—34no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—68no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—68no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—94no—
834C2×C4—92no—
835C2×C4—92no—
836C2×C4—92no—
837C2×C4—92no—
838C2×C4—188no—
839C2×C4—188no—
840C2×C4—188no—
841C2×C4—182no—
842C2×C4—182no—
843C2×C4—182no—
844C2×C4C22×D3212yes—
845C2×C3—24no—
846C2×C3—24no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—24no—
851C2×C3—44no—
852C2×C3—44no—
853C2×C3—42no—
854C2×C3—42no—
855C2×C3—122no—
856C2×C3#560014yescomplemented
857C2×C3#564914yescomplemented
858C2×C3C22×#23711yescharacteristic
859C2×C3C22×#23711yescharacteristic
860C2×C3C22×#23711yescharacteristic
861C2×C3C2×D3×#4111yescharacteristic
862C2×C3C2×D3×#4111yescharacteristic
863C2×C3C2×D3×#4111yescharacteristic
864D3—42no—
865C22—22no—
866C22—22no—
867C22—28no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—124no—
876C22D3×#23712yes—
877C22#6431212yes—
878C22C2×#380514yes—
879C22C2×#380512yes—
880C22C23×D3211yescharacteristic
881C4—22no—
882C4—34no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—94no—
890C4—182no—
891C4—182no—
892C4—182no—
893C3—21no—
894C3C2×#560011yescharacteristic, complemented
895C3C2×#564911yescharacteristic, complemented
896C2—24no—
897C2—42no—
898C2—122no—
899C2#1059520214yesdirect product factor
900C2C2×D3×#23711yescharacteristic
901C2C2×#6431211yescharacteristic
902C2C22×#380511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#939C2
hypercenterC22×D4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C2×#67⋊Dic3C2semidirect
6. C2×#63964C2semidirect
7. C2×#63961C2semidirect
8. C2×#63959C2semidirect
9. C2×#63957C2semidirect
10. C2×#63956C2semidirect
11. C22×Dic32C2semidirect
12. #10595202C2direct (N × H)
13. C2×#63878C2semidirect
14. C2×#63861C2semidirect
15. C2×#63845C2semidirect
16. C2×#63838C2semidirect
30. D4×C3⋊Dic3C22semidirect
38. C3×#935C22semidirect
43. #67⋊Dic3C22semidirect
44. #67⋊Dic3C22semidirect
51. #63964C22semidirect
52. #63961C22semidirect
56. #63959C22semidirect
57. #63957C22semidirect
58. #63956C22semidirect
64. C2×Dic32C22semidirect
65. #63878C22semidirect
66. #63861C22semidirect
67. #63845C22semidirect
68. #63838C22semidirect
74. C2×#935D3semidirect
209. #935C2×D3semidirect
661. C2×C32#529semidirect
798. C32C2×#529semidirect
856. C2×C3#5600semidirect
857. C2×C3#5649semidirect
894. C3C2×#5600semidirect
895. C3C2×#5649semidirect
899. C2#10595202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9392
C2×C3×#9352
C2×#67⋊Dic32
C2×#639642
C2×#639612
C2×#639592
C2×#639572
C2×#639562
C22×Dic322
#105952022
C2×#638782
C2×#638612
C2×#638452
C2×#638382
C2×#56493
C2×#56003