Finite Group Databasebeta

← C2×#10594218 #11903162

Subgroups — C2×#10594218 #11903162

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63906C211yesmaximal, characteristic, complemented
9C2×#63905C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63868C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63862C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594218C2116yesmaximal, direct product factor
17C2×#5540—31nomaximal
18C2×#5565—31nomaximal
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C2×C32×C22⋊C4C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35#64090C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#67⋊C4C2218yescomplemented
43C3×#67⋊C4C2218yescomplemented
44#63980C2218yescomplemented
45#63978C2218yescomplemented
46#63978C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2218yescomplemented
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61#63906C2218yescomplemented
62#63905C2218yescomplemented
63C4×#626C2218yescomplemented
64#63868C2218yescomplemented
65#63867C2218yescomplemented
66#63862C2218yescomplemented
67#63855C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×C4×D4—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#930—31no—
78C2×#929—31no—
79C2×C4×#67—31no—
80C2×#926—31no—
81C22×C4⋊Dic3—31no—
82C22×Dic3⋊C4—31no—
83#5565—316no—
84#5540—316no—
85C2×#898—31no—
86C2×#898—31no—
87C2×#894—31no—
88C2×#889—31no—
89C2×#884—31no—
90C2×#883—31no—
91C2×#883—31no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—61no—
95C2×#67⋊C4D311yescharacteristic, complemented
96C2×#67⋊C4D311yescharacteristic, complemented
97C2×#879—31no—
98C2×#876—31no—
99C2×C4×D12—31no—
100C2×#872—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C2×#638—24no—
109C2×#638C2314yes—
110C22×C3⋊Dic3—42no—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2314yes—
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×C3×#67—24no—
118C2×C3×#67—24no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C22×C3×Dic3—24no—
122C22×C3×Dic3—42no—
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3—42no—
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2314yes—
135C2×#626—24no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#625—42no—
140C2×#625C2314yes—
141C32×C22⋊C4C2314yes—
142#3752C2314yes—
143#3750C2314yes—
144C4×C3⋊Dic3C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2314yes—
150C3×C4×Dic3C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—31no—
170C23×C3×C4—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—61no—
178C22×#67C2×D311yescharacteristic
179C22×#67C2×D311yescharacteristic
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3—61no—
183C23×Dic3C2×D311yescharacteristic
184C23×Dic3C2×D311yescharacteristic
185C22×D12—31no—
186C22×D12—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—61no—
190C22×C4×D3C2×D311yescharacteristic
191C22×C4×D3C2×D311yescharacteristic
192C3×C4×D4—38no—
193C3×C4×D4—38no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C22⋊C4—21no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4C2×D311yescharacteristic
201C2×C3×C42—31no—
202C2×C3×C42—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#939—38no—
208#939—38no—
209#939—38no—
210#939—38no—
211#930—38no—
212#930—38no—
213#930—38no—
214#929—38no—
215C4×#67—38no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—61no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229#926—38no—
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—38no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—38no—
248C2×Dic3⋊C4—61no—
249C2×Dic3⋊C4C2×D311yescharacteristic
250C2×Dic3⋊C4C2×D311yescharacteristic
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—61no—
254C2×C4×Dic3C2×D311yescharacteristic
255C2×C4×Dic3C2×D311yescharacteristic
256#898—38no—
257#898—38no—
258#894—38no—
259#889—38no—
260#884—38no—
261#883—38no—
262#883—38no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#67⋊C4—68no—
266#67⋊C4C2×D318yescomplemented
267#67⋊C4C2×D318yescomplemented
268#879—38no—
269#876—38no—
270C4×D12—38no—
271#872—38no—
272#870—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4C2412yes—
293C2×C32×C4C2412yes—
294#638—28no—
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—44no—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—44no—
303C3×#67—28no—
304C3×#67—28no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—28no—
311C2×C3×Dic3—44no—
312C2×C3×Dic3#4114yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C3×C4×D3—28no—
320C3×C4×D3—44no—
321#626—28no—
322#626—44no—
323#625—44no—
324#553—916no—
325C2×#126—91no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#121—91no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—31no—
335C2×C4×D4—31no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—91no—
339C22×C4⋊C4—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—61no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×D4—34no—
351C2×C3×D4—34no—
352C2×C3×D4—64no—
353C2×C3×D4—64no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—34no—
363C22×C3×C4—34no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4—64no—
367C22×C3×C4—64no—
368C22×C3×C4—122no—
369C22×C3×C4—122no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C2×#67—24no—
375C2×#67—24no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—64no—
383C2×#67—68no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—64no—
387C2×#67—122no—
388C2×#67—122no—
389C2×#67—122no—
390C2×#67C22×D314yes—
391C2×#67C22×D314yes—
392C22×Dic3—24no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—42no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—64no—
405C22×Dic3—61no—
406C22×Dic3—122no—
407C22×Dic3—122no—
408C22×Dic3—124no—
409C22×Dic3C22×D314yes—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D314yes—
416C22×Dic3C22×D311yescharacteristic
417C2×D12—34no—
418C2×D12—34no—
419C2×D12—64no—
420C2×D12—122no—
421C2×C4×D3—24no—
422C2×C4×D3—34no—
423C2×C4×D3—34no—
424C2×C4×D3—42no—
425C2×C4×D3—64no—
426C2×C4×D3—122no—
427C2×C4×D3—122no—
428C2×C4×D3—124no—
429C2×C4×D3C22×D314yes—
430C2×C4×D3C22×D314yes—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—24no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4C22×D314yes—
437C3×C22⋊C4C22×D314yes—
438C3×C42—34no—
439C3×C42—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—64no—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—64no—
474Dic3⋊C4C22×D314yes—
475Dic3⋊C4C22×D314yes—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—64no—
479C4×Dic3C22×D314yes—
480C4×Dic3C22×D314yes—
481C22×C32—28no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32C2×#4114yes—
485C22×C32C2×#4112yes—
486C22×C32C2×#4112yes—
487C22×C32H(5,𝔽2)12yes—
488C22×C32C2511yescharacteristic
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—44no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—44no—
500C2×C3×D3—44no—
501C32×C4—22no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3C2×#4114yes—
512C22×D4—31no—
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—31no—
522C23×C4—91no—
523C23×C4—91no—
524#126—98no—
525#126—98no—
526#125—98no—
527#123—98no—
528#123—98no—
529#121—98no—
530#121—98no—
531#121—98no—
532#121—98no—
533C4×D4—38no—
534C4×D4—38no—
535C4×D4—98no—
536C4×D4—98no—
537#117—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—98no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4—91no—
548C2×C4⋊C4—91no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4D3211yescharacteristic
559C2×C42—31no—
560C2×C42—31no—
561C2×C42—91no—
562C23×C3—22no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—21no—
568C23×C3—24no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—42no—
572C23×C3—42no—
573C23×C3—62no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3#23514yes—
580C23×C3#23514yes—
581C23×C3C23×D312yes—
582C23×C3C23×D312yes—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—62no—
594C22×D3—64no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3C23×D312yes—
604C22×D3C23×D312yes—
605C3×D4—68no—
606C3×D4—68no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—34no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—42no—
621C2×C3×C4—42no—
622C2×C3×C4—68no—
623C2×C3×C4—68no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—124no—
630C2×C3×C4—124no—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635#67—28no—
636#67—28no—
637#67—616no—
638#67—68no—
639#67—68no—
640#67—68no—
641#67—124no—
642#67—124no—
643#67—124no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—28no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—44no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—64no—
661C2×Dic3—64no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—122no—
669C2×Dic3—124no—
670C2×Dic3—124no—
671C2×Dic3—128no—
672C2×Dic3#23714yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D312yes—
679D12—68no—
680D12—124no—
681C4×D3—28no—
682C4×D3—44no—
683C4×D3—124no—
684C4×D3—124no—
685C4×D3—128no—
686C2×C32—24no—
687C2×C32#55314yescomplemented
688C2×C32C22×#4111yescharacteristic
689C2×C32C22×#4111yescharacteristic
690C2×C32C2×H(5,𝔽2)11yescharacteristic
691C3⋊D3—42no—
692C3×D3—42no—
693C3×D3—42no—
694C24—31no—
695C24—31no—
696C24—91no—
697C24C2×D3211yescharacteristic
698C2×D4—34no—
699C2×D4—34no—
700C2×D4—64no—
701C2×D4—64no—
702C2×D4—94no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—94no—
706C2×D4—184no—
707C2×D4—184no—
708C2×D4—362no—
709C2×D4—362no—
710C22×C4—31no—
711C22×C4—34no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—34no—
718C22×C4—34no—
719C22×C4—34no—
720C22×C4—64no—
721C22×C4—64no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—91no—
725C22×C4—94no—
726C22×C4—94no—
727C22×C4—122no—
728C22×C4—122no—
729C22×C4—362no—
730C22×C4—362no—
731C22×C4C2×D3211yescharacteristic
732C22×C4C2×D3211yescharacteristic
733C4⋊C4—34no—
734C4⋊C4—34no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4C2×D3214yes—
753C42—34no—
754C42—34no—
755C42—94no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—28no—
761C22×C3—28no—
762C22×C3—22no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—21no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—48no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—124no—
777C22×C3—124no—
778C22×C3C2×#23514yes—
779C22×C3C2×#23514yes—
780C22×C3C2×#23512yes—
781C22×C3C2×#23512yes—
782C22×C3C2×#23712yes—
783C22×C3#100412yes—
784C22×C3D3×#4112yes—
785C22×C3#100912yes—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—44no—
795C2×D3—44no—
796C2×D3—64no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—128no—
806C2×D3—124no—
807C2×D3—124no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—34no—
813C3×C4—42no—
814C3×C4—42no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—64no—
826Dic3—64no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—62no—
833Dic3—122no—
834Dic3C2×#23714yes—
835C32C2×#55311yescharacteristic, complemented, Sylow
836C23—22no—
837C23—22no—
838C23—32no—
839C23—32no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—92no—
847C23—182no—
848C23—182no—
849C23—182no—
850C23#379814yes—
851C23C22×D3212yes—
852C23C22×D3211yescharacteristic
853D4—68no—
854D4—68no—
855D4—188no—
856D4—188no—
857D4—364no—
858D4—364no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—34no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—68no—
869C2×C4—68no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—124no—
879C2×C4—124no—
880C2×C4—182no—
881C2×C4—182no—
882C2×C4—182no—
883C2×C4—364no—
884C2×C4—364no—
885C2×C4C22×D3212yes—
886C2×C4C22×D3212yes—
887C2×C3—24no—
888C2×C3—24no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—24no—
893C2×C3—44no—
894C2×C3—122no—
895C2×C3—122no—
896C2×C3#554014yescomplemented
897C2×C3#556514yescomplemented
898C2×C3C22×#23511yescharacteristic
899C2×C3C22×#23511yescharacteristic
900C2×C3C22×#23711yescharacteristic
901C2×C3C2×#100411yescharacteristic
902C2×C3C2×D3×#4111yescharacteristic
903C2×C3C2×#100911yescharacteristic
904D3—42no—
905D3—42no—
906D3—124no—
907D3—122no—
908D3—122no—
909C22—22no—
910C22—22no—
911C22—28no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22—62no—
918C22—124no—
919C22—124no—
920C22—182no—
921C22—182no—
922C22—182no—
923C22—364no—
924C22C2×#379814yes—
925C22C2×#379812yes—
926C22D3×#23712yes—
927C22#6431412yes—
928C22C23×D3211yescharacteristic
929C4—22no—
930C4—22no—
931C4—34no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—182no—
938C4—182no—
939C4—182no—
940C3—21no—
941C3C2×#556511yescharacteristic, complemented
942C3C2×#554011yescharacteristic, complemented
943C2—24no—
944C2—122no—
945C2—122no—
946C2—362no—
947C2#1059421814yesdirect product factor
948C2C22×#379811yescharacteristic
949C2C2×D3×#23711yescharacteristic
950C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#553
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×#64090C2semidirect
2. C2×C3×#67⋊C4C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×#63980C2semidirect
5. C2×#63978C2semidirect
6. C2×#63978C2semidirect
7. C22×Dic3⋊Dic3C2semidirect
8. C2×#63906C2semidirect
9. C2×#63905C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63868C2semidirect
12. C2×#63867C2semidirect
13. C2×#63862C2semidirect
14. C2×#63855C2semidirect
15. C2×#63853C2semidirect
16. #10594218C2direct (N × H)
35. #64090C22semidirect
42. C3×#67⋊C4C22semidirect
43. C3×#67⋊C4C22semidirect
44. #63980C22semidirect
45. #63978C22semidirect
46. #63978C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
61. #63906C22semidirect
62. #63905C22semidirect
63. C4×#626C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
66. #63862C22semidirect
67. #63855C22semidirect
68. #63853C22semidirect
95. C2×#67⋊C4D3semidirect
96. C2×#67⋊C4D3semidirect
266. #67⋊C4C2×D3semidirect
267. #67⋊C4C2×D3semidirect
687. C2×C32#553semidirect
835. C32C2×#553semidirect
896. C2×C3#5540semidirect
897. C2×C3#5565semidirect
941. C3C2×#5565semidirect
942. C3C2×#5540semidirect
947. C2#10594218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640902
C2×C3×#67⋊C42
C2×#639802
C2×#639782
C22×Dic3⋊Dic32
C2×#639062
C2×#639052
C2×C4×#6262
C2×#638682
C2×#638672
C2×#638622
C2×#638552
C2×#638532
#105942182
C2×#55403
C2×#55653