Finite Group Databasebeta

← C2×#10594951 #11903259

Subgroups — C2×#10594951 #11903259

Order 1152.

2561 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C211yesmaximal, characteristic
5C2×Dic3×#67C211yesmaximal, characteristic
6C2×#63964C211yesmaximal, characteristic, complemented
7C2×#63964C211yesmaximal, characteristic, complemented
8#10594951C2116yesmaximal, direct product factor
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63893C211yesmaximal, characteristic, complemented
11C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63851C211yesmaximal, characteristic, complemented
14C2×#63845C211yesmaximal, characteristic, complemented
15C2×#63840C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5539—31nomaximal
18C2×#5511—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
32#64133C2218yescomplemented
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C3×C4×#67C2218yes—
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2218yescomplemented
44C2×C3×C4×Dic3C2211yescharacteristic
45Dic3×#67C2218yes—
46Dic3×#67C2218yes—
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55#63964C2218yescomplemented
56#63964C2218yescomplemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63896C2218yescomplemented
62#63893C2218yescomplemented
63D3×Dic3⋊C4C2218yescomplemented
64#63867C2218yescomplemented
65#63851C2218yescomplemented
66#63845C2218yescomplemented
67#63840C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×C4×D4—31no—
70C22×C3×C4⋊C4—31no—
71C2×D4×Dic3—31no—
72C2×D4×Dic3—31no—
73C2×C4×#67—31no—
74C2×C4×#67—31no—
75C2×C4×#67D311yescharacteristic
76C2×#924—31no—
77C2×#924—31no—
78C2×#924—31no—
79C2×#924—31no—
80C2×#924—31no—
81C2×#924—61no—
82C22×Dic3⋊C4—31no—
83C22×Dic3⋊C4D311yescharacteristic, complemented
84#5539—316no—
85#5511—316no—
86C2×#897—31no—
87C2×#896—31no—
88C2×#896—31no—
89C2×D3×C4⋊C4—31no—
90C2×#890—31no—
91C2×#889—31no—
92C2×#889—31no—
93C2×#888—31no—
94C2×#888—31no—
95C2×#887—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#870—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4—42no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2314yes—
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—42no—
113C2×#634C2314yes—
114C2×C3×#67Q818yescomplemented
115C2×C3×#67C2314yes—
116C22×C3×Dic3—24no—
117C22×C3×Dic3—42no—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3C2314yes—
129C2×#627—24no—
130C2×#627—42no—
131C2×#627C2314yes—
132C2×#627C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3—42no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137#3757C2314yes—
138#3757C2314yes—
139C4⋊(C3⋊Dic3)C2314yes—
140#3750C2314yes—
141#3750C2314yes—
142C3×#217C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161Dic32C2314yes—
162C2×#554—91noSylow
163C22×C3×D4—31no—
164C23×C3×C4—21no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—31no—
168C23×C3×C4C2×D311yescharacteristic
169C23×C3×C4C2×D311yescharacteristic
170C22×#67C2×D311yescharacteristic
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3C2×D311yescharacteristic
174C23×Dic3C2×D311yescharacteristic
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3C2×D311yescharacteristic
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6—31no—
184C22×Dic6—61no—
185C3×C4×D4—38no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—38no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C42—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—61no—
202C2×#217—61no—
203C2×#217C2×D311yescharacteristic
204D4×Dic3—38no—
205D4×Dic3—38no—
206C4×#67—38no—
207C4×#67—38no—
208C4×#67C2×D318yes—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—61no—
221#924—38no—
222#924—38no—
223#924—38no—
224#924—38no—
225#924—38no—
226#924—68no—
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⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—38no—
242C2×Dic3⋊C4—61no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×Dic3⋊C4C2×D318yescomplemented
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic
255#897—38no—
256#896—38no—
257#896—38no—
258D3×C4⋊C4—38no—
259#890—38no—
260#889—38no—
261#889—38no—
262#888—38no—
263#888—38no—
264#887—38no—
265#878—38no—
266#878—38no—
267#878—38no—
268#878—38no—
269#870—38no—
270C4×Dic6—38no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2×Q814yes—
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3C2×Q814yes—
279C22×C3×D3C2412yes—
280C2×C32×C4—22no—
281C2×C32×C4—22no—
282C2×C32×C4—44no—
283C2×C32×C4C2412yes—
284C2×C32×C4C2412yes—
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3—22no—
287C2×C3⋊Dic3—22no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3C2412yes—
290C2×C3⋊Dic3C2412yes—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293#634—44no—
294C3×#67C2×Q8116yescomplemented
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3—44no—
302C2×C3×Dic3C2×Q814yes—
303C2×C3×Dic3#4114yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—44no—
312#627—28no—
313#627—44no—
314D3×Dic3—28no—
315D3×Dic3—44no—
316#554—916no—
317C2×C4⋊Q8—91no—
318C2×#125—91no—
319C2×#125—91no—
320C2×C22⋊Q8—91no—
321C2×C22⋊Q8—91no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C2×C22⋊Q8—91no—
325C2×C22⋊Q8—91no—
326C2×C4×Q8—91no—
327C2×C4×D4—31no—
328C2×C4×D4—91no—
329C2×C4×D4—91no—
330C22×C4⋊C4—31no—
331C22×C4⋊C4—91no—
332C24×C3—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C2×C3×D4—38no—
338C2×C3×D4—34no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—24no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—42no—
353C22×C3×C4—42no—
354C22×C3×C4—44no—
355C22×C3×C4—64no—
356C22×C3×C4—122no—
357C22×C3×C4—122no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D314yes—
363C22×C3×C4C22×D314yes—
364C2×#67Dic618yescomplemented
365C2×#67C22×D314yes—
366C22×Dic3—24no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—34no—
376C22×Dic3—34no—
377C22×Dic3—42no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—64no—
383C22×Dic3—122no—
384C22×Dic3C22×D314yes—
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D314yes—
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C2×C4×D3—34no—
394C2×C4×D3—34no—
395C2×C4×D3—42no—
396C2×C4×D3—64no—
397C2×C4×D3—122no—
398C2×C4×D3C22×D314yes—
399C2×Dic6—34no—
400C2×Dic6—34no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—34no—
404C2×Dic6—34no—
405C2×Dic6—64no—
406C2×Dic6—64no—
407C2×Dic6—64no—
408C2×Dic6—122no—
409C2×Dic6—122no—
410C2×Dic6—122no—
411C2×Dic6—122no—
412C2×Dic6—124no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C42—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—34no—
426#217—34no—
427#217—64no—
428#217—64no—
429#217C22×D314yes—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4C22×D314yes—
433C4⋊Dic3—34no—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
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⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—64no—
457Dic3⋊C4—64no—
458Dic3⋊C4C22×D314yes—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3C22×D314yes—
468C22×C32—28no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32C22×Q814yes—
472C22×C32C22×Q812yes—
473C22×C32C2×#4112yes—
474C22×C32H(5,𝔽2)12yes—
475C22×C32C2511yescharacteristic
476C2×C3×D3—28no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3C22×Q814yes—
480C32×C4—22no—
481C32×C4—22no—
482C3⋊Dic3—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3C22×Q814yes—
492C3×Dic3C2×#4114yes—
493C22×Q8—91no—
494C22×Q8—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502C23×C4D3211yescharacteristic
503C4⋊Q8—98no—
504#125—98no—
505#125—98no—
506C22⋊Q8—98no—
507C22⋊Q8—98no—
508C22⋊Q8—98no—
509C22⋊Q8—98no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512C4×Q8—98no—
513C4×D4—38no—
514C4×D4—98no—
515C4×D4—98no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—38no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—98no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—91no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C42—31no—
541C2×C42—91no—
542C2×C42—91no—
543C23×C3—22no—
544C23×C3—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—21no—
549C23×C3—24no—
550C23×C3—34no—
551C23×C3—32no—
552C23×C3—42no—
553C23×C3—42no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3C2×Dic614yes—
557C23×C3D3×Q814yes—
558C23×C3C23×D312yes—
559C23×C3C23×D312yes—
560C23×C3C23×D311yescharacteristic
561C23×C3C23×D311yescharacteristic
562C22×D3—22no—
563C22×D3—22no—
564C22×D3C2×Dic614yes—
565C22×D3C23×D312yes—
566C3×D4—316no—
567C2×C3×C4—24no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—42no—
584C2×C3×C4—44no—
585C2×C3×C4—44no—
586C2×C3×C4—48no—
587C2×C3×C4—68no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—124no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599#67C2×Dic6116yescomplemented
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—22no—
603C2×Dic3—22no—
604C2×Dic3—22no—
605C2×Dic3—28no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—44no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—62no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—68no—
628C2×Dic3—122no—
629C2×Dic3—122no—
630C2×Dic3—122no—
631C2×Dic3—122no—
632C2×Dic3—124no—
633C2×Dic3C2×Dic614yes—
634C2×Dic3#23514yes—
635C2×Dic3C23×D312yes—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C4×D3—44no—
643C4×D3—68no—
644C4×D3—124no—
645Dic6—68no—
646Dic6—68no—
647Dic6—124no—
648Dic6—124no—
649Dic6—124no—
650Dic6—124no—
651Dic6—128no—
652C2×C32—24no—
653C2×C32#55414yescomplemented
654C2×C32C23×Q811yescharacteristic
655C2×C32C22×#4111yescharacteristic
656C2×C32C2×H(5,𝔽2)11yescharacteristic
657C3×D3—24no—
658C24—31no—
659C24C2×D3211yescharacteristic
660C2×Q8—94no—
661C2×Q8—94no—
662C2×Q8—94no—
663C2×Q8—184no—
664C2×Q8—362no—
665C2×Q8—362no—
666C2×D4—34no—
667C2×D4—38no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—34no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—34no—
677C22×C4—34no—
678C22×C4—42no—
679C22×C4—64no—
680C22×C4—94no—
681C22×C4—94no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—122no—
687C22×C4—122no—
688C22×C4—184no—
689C22×C4—362no—
690C22×C4C2×D3211yescharacteristic
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3214yes—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
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—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C42—34no—
716C42—94no—
717C42—94no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—28no—
723C22×C3—28no—
724C22×C3—22no—
725C22×C3—24no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—34no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3—48no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—68no—
736C22×C3C22×Dic614yes—
737C22×C3C22×Dic612yes—
738C22×C3C2×#23512yes—
739C22×C3#100412yes—
740C22×C3#100412yes—
741C22×C3C2×D3×Q814yes—
742C22×C3C2×D3×Q812yes—
743C22×C3D3×#4112yes—
744C22×C3C24×D311yescharacteristic
745C22×C3C24×D311yescharacteristic
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—28no—
749C2×D3C22×Dic614yes—
750C3×C4—24no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—34no—
756C3×C4—34no—
757C3×C4—42no—
758C3×C4—62no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763Dic3—22no—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—62no—
769Dic3—62no—
770Dic3—62no—
771Dic3—62no—
772Dic3—62no—
773Dic3—62no—
774Dic3—62no—
775Dic3—62no—
776Dic3—122no—
777Dic3—122no—
778Dic3—122no—
779Dic3—122no—
780Dic3C22×Dic614yes—
781Dic3C2×#23514yes—
782C32C2×#55411yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—34no—
786C23—32no—
787C23—62no—
788C23—62no—
789C23D3×Dic614yes—
790C23C22×D3212yes—
791C23C22×D3211yescharacteristic
792Q8—188no—
793Q8—364no—
794Q8—364no—
795D4—316no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—34no—
799C2×C4—34no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—44no—
808C2×C4—68no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—92no—
815C2×C4—92no—
816C2×C4—92no—
817C2×C4—92no—
818C2×C4—124no—
819C2×C4—124no—
820C2×C4—188no—
821C2×C4—182no—
822C2×C4—182no—
823C2×C4—182no—
824C2×C4—182no—
825C2×C4—364no—
826C2×C4C22×D3212yes—
827C2×C4C22×D3212yes—
828C2×C3—24no—
829C2×C3—24no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—24no—
834C2×C3—44no—
835C2×C3—64no—
836C2×C3#551114yescomplemented
837C2×C3#553914yescomplemented
838C2×C3C23×Dic611yescharacteristic
839C2×C3C22×#23511yescharacteristic
840C2×C3C2×#100411yescharacteristic
841C2×C3C2×#100411yescharacteristic
842C2×C3C22×D3×Q811yescharacteristic
843C2×C3C2×D3×#4111yescharacteristic
844D3—24no—
845C22—22no—
846C22—22no—
847C22—28no—
848C22—34no—
849C22—62no—
850C22—62no—
851C22—68no—
852C22C2×D3×Dic614yes—
853C22C2×D3×Dic612yes—
854C22D3×#23512yes—
855C22#6433012yes—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—22no—
859C4—34no—
860C4—34no—
861C4—62no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—182no—
867C4—182no—
868C4—182no—
869C4—182no—
870C3—21no—
871C3C2×#551111yescharacteristic, complemented
872C3C2×#553911yescharacteristic, complemented
873C2—24no—
874C2—64no—
875C2#1059495114yesdirect product factor
876C2C22×D3×Dic611yescharacteristic
877C2C2×D3×#23511yescharacteristic
878C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C22×C3×Dic3⋊C4C2semidirect
6. C2×#63964C2semidirect
7. C2×#63964C2semidirect
8. #10594951C2direct (N × H)
9. C2×#63896C2semidirect
10. C2×#63893C2semidirect
11. C2×D3×Dic3⋊C4C2semidirect
12. C2×#63867C2semidirect
13. C2×#63851C2semidirect
14. C2×#63845C2semidirect
15. C2×#63840C2semidirect
16. C2×#63837C2semidirect
32. #64133C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
55. #63964C22semidirect
56. #63964C22semidirect
61. #63896C22semidirect
62. #63893C22semidirect
63. D3×Dic3⋊C4C22semidirect
64. #63867C22semidirect
65. #63851C22semidirect
66. #63845C22semidirect
67. #63840C22semidirect
68. #63837C22semidirect
83. C22×Dic3⋊C4D3semidirect
114. C2×C3×#67Q8semidirect
249. C2×Dic3⋊C4C2×D3semidirect
294. C3×#67C2×Q8semidirect
364. C2×#67Dic6semidirect
599. #67C2×Dic6semidirect
653. C2×C32#554semidirect
782. C32C2×#554semidirect
836. C2×C3#5511semidirect
837. C2×C3#5539semidirect
871. C3C2×#5511semidirect
872. C3C2×#5539semidirect
875. C2#10594951direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×C4×#672
C22×C3×Dic3⋊C42
C2×Dic3×#672
C2×#639642
#105949512
C2×#638962
C2×#638932
C2×D3×Dic3⋊C42
C2×#638672
C2×#638512
C2×#638452
C2×#638402
C2×#638372
C2×#55393
C2×#55113