Finite Group Databasebeta

← C2×#87055 #11703391

Subgroups — C2×#87055 #11703391

Order 768.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic, complemented
2#87055C2132yesmaximal, direct product factor
3C2×#5718C211yesmaximal, characteristic, complemented
4C2×#5716C211yesmaximal, characteristic, complemented
5C2×#5677C212yesmaximal, complemented
6C2×#5682C212yesmaximal, complemented
7C2×#5681C212yesmaximal, complemented
8C2×#5680C212yesmaximal, complemented
9C2×#5655C214yesmaximal, complemented
10C2×#5662C214yesmaximal, complemented
11C2×#5579C211yesmaximal, characteristic, complemented
12C2×#5580C211yesmaximal, characteristic, complemented
13C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
14C2×Q8×Dic6C211yesmaximal, characteristic, complemented
15C2×#5551C212yesmaximal, complemented
16C2×#5548C212yesmaximal, complemented
17C2×#5539C212yesmaximal, complemented
18C2×#5546C212yesmaximal, complemented
19C2×#3522—31nomaximal, Sylow
20C22×D3×Q8C2211yescharacteristic
21C22×#237C2212yes—
22C22×#237C2212yes—
23C22×#235C2214yes—
24C3×#559C22116yescomplemented
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124C2212yes—
27C2×C3×#124C2212yes—
28C2×C3×#123C2214yes—
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2212yes—
32C2×C3×C4×D4C2212yes—
33C2×#947C2211yescharacteristic
34C2×#946C2211yescharacteristic
35C2×#946C2212yes—
36C2×Q8×Dic3C2212yes—
37C2×Q8×Dic3C2211yescharacteristic
38C2×#940C2212yes—
39C2×#939C2214yes—
40C2×#938C2212yes—
41C2×#938C2212yes—
42C2×#938C2212yes—
43C2×#936C2212yes—
44C2×D4×Dic3C2212yes—
45C2×D4×Dic3C2212yes—
46C2×D4×Dic3C2212yes—
47C2×C4×#67C2214yes—
48C2×#924C2214yes—
49C22×Dic3⋊C4C2214yes—
50#5718C22116yescomplemented
51#5716C22116yescomplemented
52#5682C22132yescomplemented
53#5681C22132yescomplemented
54#5680C22132yescomplemented
55#5677C22132yescomplemented
56#5662C22164yescomplemented
57#5655C22164yescomplemented
58#5580C22116yescomplemented
59#5579C22116yescomplemented
60C4×D3×Q8C22116yescomplemented
61Q8×Dic6C22116yescomplemented
62#5551C22132yescomplemented
63#5548C22132yescomplemented
64#5546C22132yescomplemented
65#5539C22132yescomplemented
66C2×#898C2212yes—
67C2×#896C2214yes—
68C2×#895C2211yescharacteristic
69C2×#894C2212yes—
70C2×D3×C4⋊C4C2211yescharacteristic
71C2×D3×C4⋊C4C2212yes—
72C2×D3×C4⋊C4C2212yes—
73C2×#890C2211yescharacteristic
74C2×#888C2212yes—
75C2×#888C2214yes—
76C2×#887C2212yes—
77C2×#887C2211yescharacteristic
78C2×#886C2214yes—
79C2×#885C2214yes—
80C2×#885C2214yes—
81C2×#884C2214yes—
82C2×#883C2214yes—
83C2×#883C2214yes—
84C2×#67⋊C4C2214yes—
85C2×#67⋊C4C2214yes—
86C2×#879C2214yes—
87C2×#878C2214yes—
88C2×#878C2214yes—
89C2×#877C2214yes—
90C2×C4×D12C2212yes—
91C2×C4×D12C2212yes—
92C2×C4×D12C2211yescharacteristic
93C2×#872C2212yes—
94C2×C42×D3C2212yes—
95C2×C42×D3C2211yescharacteristic
96C2×#870C2212yes—
97C2×#869C2212yes—
98C2×#869C2211yescharacteristic
99C2×C4×Dic6C2212yes—
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2212yes—
102#3522—332no—
103C2×#559—32no—
104C2×#559D311yescharacteristic, complemented
105C2×Q82—31no—
106C2×#554—31no—
107C2×#554—32no—
108C2×#550—31no—
109C2×#548—32no—
110C2×#547—34no—
111C2×#547—32no—
112C2×#542—32no—
113C2×#542—34no—
114C2×#532—31no—
115C2×#532—32no—
116C2×#529—32no—
117C2×#529—31no—
118C2×#520—32no—
119C22×C4×Q8—31no—
120C22×C3×Q8C2311yescharacteristic
121C22×C3×Q8C2311yescharacteristic
122C22×C3×D4C2312yes—
123C22×C3×D4C2312yes—
124C22×C3×D4C2312yes—
125C23×C3×C4C2314yes—
126C22×#67C2314yes—
127C22×#67C2314yes—
128C22×#67C2314yes—
129C23×Dic3C2314yes—
130C23×Dic3C2314yes—
131C2×D3×Q8—28no—
132C2×D3×Q8C2318yes—
133C2×#237—216no—
134C2×#237—48no—
135C2×#237C23116yes—
136C2×#237C23116yes—
137C2×#235—416no—
138C2×#235C23132yes—
139C22×D12C2312yes—
140C22×D12C2311yescharacteristic
141C22×C4×D3C2312yes—
142C22×C4×D3C2311yescharacteristic
143C22×C4×D3C2312yes—
144C22×C4×D3C2311yescharacteristic
145C22×C4×D3C2312yes—
146C22×C4×D3C2311yescharacteristic
147C22×C4×D3C2314yes—
148C22×Dic6C2312yes—
149C22×Dic6C2314yes—
150C22×Dic6C2312yes—
151C22×Dic6C2311yescharacteristic
152C3×#127C2318yes—
153C3×#124C23116yes—
154C3×#124C23116yes—
155C3×#123C23132yes—
156C3×C4×Q8C2318yes—
157C3×C4×Q8C2318yes—
158C3×C4×D4C23116yes—
159C3×C4×D4C23116yes—
160C2×C3×C4⋊C4C2311yescharacteristic
161C2×C3×C4⋊C4C2312yes—
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C4⋊C4C2312yes—
164C2×C3×C22⋊C4C2314yes—
165C2×C3×C22⋊C4C2314yes—
166C2×C3×C22⋊C4C2314yes—
167C2×C3×C42C2311yescharacteristic
168C2×C3×C42C2312yes—
169C2×C3×C42C2312yes—
170C2×#217C2314yes—
171C2×#217C2314yes—
172C2×#217C2314yes—
173#947C2318yes—
174#946C23116yes—
175#946C2318yes—
176Q8×Dic3C23116yes—
177Q8×Dic3C2318yes—
178#940C23116yes—
179#939C23132yes—
180#938C23116yes—
181#938C23116yes—
182#938C23116yes—
183#936C23116yes—
184D4×Dic3C23116yes—
185D4×Dic3C23116yes—
186D4×Dic3C23116yes—
187C4×#67C23132yes—
188C2×(C2×D3)⋊C4C2312yes—
189C2×(C2×D3)⋊C4C2312yes—
190C2×(C2×D3)⋊C4C2312yes—
191C2×(C2×D3)⋊C4C2312yes—
192C2×(C2×D3)⋊C4C2314yes—
193C2×(C2×D3)⋊C4C2312yes—
194C2×C4⋊Dic3C2312yes—
195C2×C4⋊Dic3C2311yescharacteristic
196C2×C4⋊Dic3C2312yes—
197C2×C4⋊Dic3C2312yes—
198C2×C4⋊Dic3C2314yes—
199C2×C4⋊Dic3C2311yescharacteristic
200C2×C4⋊Dic3C2312yes—
201#924C23132yes—
202C2×Dic3⋊C4C23132yes—
203C2×Dic3⋊C4C2314yes—
204C2×Dic3⋊C4C2312yes—
205C2×Dic3⋊C4C2312yes—
206C2×Dic3⋊C4C2312yes—
207C2×Dic3⋊C4C2314yes—
208C2×Dic3⋊C4C2314yes—
209C2×Dic3⋊C4C2312yes—
210C2×Dic3⋊C4C2312yes—
211C2×C4×Dic3C2312yes—
212C2×C4×Dic3C2311yescharacteristic
213C2×C4×Dic3C2314yes—
214C2×C4×Dic3C2311yescharacteristic
215C2×C4×Dic3C2312yes—
216C2×C4×Dic3C2312yes—
217C2×C4×Dic3C2311yescharacteristic
218#898C23116yes—
219#896C23132yes—
220#895C2318yes—
221#894C23116yes—
222D3×C4⋊C4C23116yes—
223D3×C4⋊C4C23116yes—
224D3×C4⋊C4C2318yes—
225#890C2318yes—
226#888C23132yes—
227#888C23116yes—
228#887C23116yes—
229#887C2318yes—
230#886C23132yes—
231#885C23132yes—
232#885C23132yes—
233#884C23132yes—
234#883C23132yes—
235#883C23132yes—
236#67⋊C4C23132yes—
237#67⋊C4C23132yes—
238#879C23132yes—
239#878C23132yes—
240#878C23132yes—
241#877C23132yes—
242C4×D12C23116yes—
243C4×D12C23116yes—
244C4×D12C2318yes—
245#872C23116yes—
246C42×D3C23116yes—
247C42×D3C2318yes—
248#870C23116yes—
249#869C23116yes—
250#869C2318yes—
251C4×Dic6C23116yes—
252C4×Dic6C23116yes—
253C4×Dic6C2318yes—
254C22×#41—32no—
255C22×#41—32no—
256C22×#41—34no—
257C23×Q8—31no—
258#559—332no—
259#559C2×D3116yescomplemented
260Q82—316no—
261#554—316no—
262#554—332no—
263#550—316no—
264#548—332no—
265#547—364no—
266#547—332no—
267#542—332no—
268#542—364no—
269#532—316no—
270#532—332no—
271C2×C4⋊Q8—32no—
272C2×C4⋊Q8—34no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—32no—
275C2×#127—32no—
276C2×#127C2×D311yescharacteristic
277#529—332no—
278#529—316no—
279C2×#126—32no—
280C2×#126—34no—
281C2×#125—31no—
282C2×#125—32no—
283C2×#124—31no—
284C2×#124—32no—
285C2×#124—34no—
286C2×#124—34no—
287C2×#124C2×D312yes—
288C2×#124C2×D312yes—
289C2×#123—32no—
290C2×#123—34no—
291C2×#123—34no—
292C2×#123—34no—
293C2×#123C2×D314yes—
294C2×C22⋊Q8—31no—
295C2×C22⋊Q8—32no—
296C2×C22⋊Q8—34no—
297C2×C22⋊Q8—34no—
298C2×C22⋊Q8—34no—
299C2×C22⋊Q8—34no—
300C2×#121—32no—
301C2×#121—32no—
302C2×#121—32no—
303C2×#121—34no—
304C2×#121—31no—
305C2×#121—34no—
306#520—332no—
307C2×C4×Q8—31no—
308C2×C4×Q8—32no—
309C2×C4×Q8—316no—
310C2×C4×Q8—31no—
311C2×C4×Q8—32no—
312C2×C4×Q8—31no—
313C2×C4×Q8—32no—
314C2×C4×Q8—32no—
315C2×C4×Q8C2×D311yescharacteristic
316C2×C4×Q8C2×D311yescharacteristic
317C2×C4×D4—32no—
318C2×C4×D4—32no—
319C2×C4×D4—32no—
320C2×C4×D4—34no—
321C2×C4×D4—34no—
322C2×C4×D4—34no—
323C2×C4×D4—32no—
324C2×C4×D4—31no—
325C2×C4×D4—32no—
326C2×C4×D4C2×D312yes—
327C2×C4×D4C2×D312yes—
328C2×#117—34no—
329C2×#117—32no—
330C22×C4⋊C4—34no—
331C22×C4⋊C4—32no—
332C22×C4⋊C4—31no—
333C22×C4⋊C4—32no—
334C22×C42—31no—
335C22×C42—32no—
336C24×C3C2414yes—
337C23×D3C2412yes—
338C23×D3C2411yescharacteristic
339C2×C3×Q8—24no—
340C2×C3×Q8—24no—
341C2×C3×Q8C2414yes—
342C2×C3×Q8C2414yes—
343C2×C3×D4—28no—
344C2×C3×D4—28no—
345C2×C3×D4—44no—
346C2×C3×D4C2418yes—
347C2×C3×D4C2418yes—
348C2×C3×D4C2418yes—
349C22×C3×C4—48no—
350C22×C3×C4C2412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2412yes—
353C22×C3×C4C2411yescharacteristic
354C22×C3×C4C2412yes—
355C22×C3×C4C24116yes—
356C22×C3×C4C2411yescharacteristic
357C22×C3×C4C2411yescharacteristic
358C2×#67—216no—
359C2×#67—216no—
360C2×#67—48no—
361C2×#67C24116yes—
362C2×#67C24116yes—
363C2×#67C24116yes—
364C22×Dic3—216no—
365C22×Dic3—48no—
366C22×Dic3C24116yes—
367C22×Dic3C2411yescharacteristic
368C22×Dic3C2411yescharacteristic
369C22×Dic3C2412yes—
370C22×Dic3C2411yescharacteristic
371C22×Dic3C2414yes—
372C22×Dic3C2412yes—
373C22×Dic3C24116yes—
374C22×Dic3C2412yes—
375D3×Q8—232no—
376#237—264no—
377#237—432no—
378#235—464no—
379C2×D12—28no—
380C2×D12—24no—
381C2×D12C2414yes—
382C2×D12C2418yes—
383C2×C4×D3—28no—
384C2×C4×D3—24no—
385C2×C4×D3—28no—
386C2×C4×D3—24no—
387C2×C4×D3—24no—
388C2×C4×D3—28no—
389C2×C4×D3—48no—
390C2×C4×D3C2414yes—
391C2×C4×D3C2414yes—
392C2×C4×D3C2418yes—
393C2×C4×D3C2418yes—
394C2×C4×D3C2414yes—
395C2×C4×D3C2418yes—
396C2×C4×D3C24116yes—
397C2×Dic6—28no—
398C2×Dic6—48no—
399C2×Dic6—44no—
400C2×Dic6#4118yescomplemented
401C2×Dic6C2418yes—
402C2×Dic6C24116yes—
403C2×Dic6C2418yes—
404C2×Dic6C2414yes—
405C3×C4⋊C4C2414yes—
406C3×C4⋊C4C2418yes—
407C3×C4⋊C4C2414yes—
408C3×C4⋊C4C2418yes—
409C3×C22⋊C4C24116yes—
410C3×C22⋊C4C24116yes—
411C3×C22⋊C4C24116yes—
412C3×C42C2414yes—
413C3×C42C2418yes—
414C3×C42C2418yes—
415#217C24116yes—
416#217C24116yes—
417#217C24116yes—
418(C2×D3)⋊C4C2418yes—
419(C2×D3)⋊C4C2418yes—
420(C2×D3)⋊C4C2418yes—
421(C2×D3)⋊C4C2418yes—
422(C2×D3)⋊C4C24116yes—
423(C2×D3)⋊C4C2418yes—
424C4⋊Dic3C2418yes—
425C4⋊Dic3C2414yes—
426C4⋊Dic3C2418yes—
427C4⋊Dic3C2418yes—
428C4⋊Dic3C24116yes—
429C4⋊Dic3C2414yes—
430C4⋊Dic3C2418yes—
431Dic3⋊C4C24116yes—
432Dic3⋊C4C2418yes—
433Dic3⋊C4C2418yes—
434Dic3⋊C4C2418yes—
435Dic3⋊C4C24116yes—
436Dic3⋊C4C24116yes—
437Dic3⋊C4C2418yes—
438Dic3⋊C4C2418yes—
439C4×Dic3C2418yes—
440C4×Dic3C2414yes—
441C4×Dic3C24116yes—
442C4×Dic3C2414yes—
443C4×Dic3C2418yes—
444C4×Dic3C2418yes—
445C4×Dic3C2414yes—
446C2×#41—316no—
447C2×#41—316no—
448C2×#41—332no—
449C2×#41—616no—
450C2×#41—1216no—
451C2×#41—128no—
452C22×Q8—38no—
453C22×Q8—31no—
454C22×Q8—32no—
455C22×Q8—34no—
456C22×Q8—32no—
457C22×Q8—68no—
458C22×Q8C22×D311yescharacteristic
459C22×Q8C22×D311yescharacteristic
460C22×D4—34no—
461C22×D4—34no—
462C22×D4—34no—
463C22×D4—31no—
464C22×D4—32no—
465C22×D4C22×D312yes—
466C22×D4C22×D312yes—
467C22×D4C22×D312yes—
468C23×C4—34no—
469C23×C4—34no—
470C23×C4—31no—
471C23×C4—32no—
472C23×C4—32no—
473C23×C4—32no—
474C23×C4—31no—
475C23×C4—31no—
476C23×C4—34no—
477C23×C4C22×D314yes—
478C4⋊Q8—316no—
479C4⋊Q8—332no—
480C4⋊Q8—38no—
481C4⋊Q8—316no—
482#127—316no—
483#127C22×D318yes—
484#126—316no—
485#126—332no—
486#125—38no—
487#125—316no—
488#124—38no—
489#124—316no—
490#124—332no—
491#124—332no—
492#124C22×D3116yes—
493#124C22×D3116yes—
494#123—316no—
495#123—332no—
496#123—332no—
497#123—332no—
498#123C22×D3132yes—
499C22⋊Q8—38no—
500C22⋊Q8—316no—
501C22⋊Q8—332no—
502C22⋊Q8—332no—
503C22⋊Q8—332no—
504C22⋊Q8—332no—
505#121—316no—
506#121—316no—
507#121—316no—
508#121—332no—
509#121—38no—
510#121—332no—
511C4×Q8—38no—
512C4×Q8—316no—
513C4×Q8—38no—
514C4×Q8—316no—
515C4×Q8—38no—
516C4×Q8—316no—
517C4×Q8—316no—
518C4×Q8C22×D318yes—
519C4×Q8C22×D318yes—
520C4×D4—316no—
521C4×D4—316no—
522C4×D4—316no—
523C4×D4—332no—
524C4×D4—332no—
525C4×D4—332no—
526C4×D4—316no—
527C4×D4—38no—
528C4×D4—316no—
529C4×D4C22×D3116yes—
530C4×D4C22×D3116yes—
531#117—332no—
532#117—316no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—32no—
535C2×C4⋊C4—34no—
536C2×C4⋊C4—34no—
537C2×C4⋊C4—32no—
538C2×C4⋊C4—32no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—32no—
542C2×C4⋊C4—332no—
543C2×C4⋊C4—32no—
544C2×C4⋊C4—31no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—34no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—34no—
549C2×C4⋊C4—316no—
550C2×C4⋊C4—38no—
551C2×C4⋊C4—316no—
552C2×C4⋊C4C22×D311yescharacteristic
553C2×C4⋊C4C22×D312yes—
554C2×C4⋊C4C22×D311yescharacteristic
555C2×C4⋊C4C22×D312yes—
556C2×C22⋊C4—34no—
557C2×C22⋊C4—34no—
558C2×C22⋊C4—34no—
559C2×C22⋊C4—32no—
560C2×C22⋊C4—32no—
561C2×C22⋊C4—32no—
562C2×C22⋊C4—32no—
563C2×C22⋊C4—34no—
564C2×C22⋊C4—32no—
565C2×C22⋊C4C22×D314yes—
566C2×C22⋊C4C22×D314yes—
567C2×C22⋊C4C22×D314yes—
568C2×C42—32no—
569C2×C42—31no—
570C2×C42—34no—
571C2×C42—31no—
572C2×C42—32no—
573C2×C42—31no—
574C2×C42—32no—
575C2×C42—38no—
576C2×C42—316no—
577C2×C42C22×D312yes—
578C2×C42C22×D312yes—
579C2×C42C22×D311yescharacteristic
580C23×C3—28no—
581C23×C3—28no—
582C23×C3—28no—
583C23×C3C2518yes—
584C23×C3C2511yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—24no—
588C22×D3—24no—
589C22×D3—24no—
590C22×D3H(5,𝔽2)14yes—
591C22×D3C2514yes—
592C22×D3C2512yes—
593C3×Q8—28no—
594C3×Q8—28no—
595C3×D4—216no—
596C3×D4—216no—
597C3×D4—48no—
598C2×C3×C4—24no—
599C2×C3×C4—22no—
600C2×C3×C4—24no—
601C2×C3×C4—24no—
602C2×C3×C4—24no—
603C2×C3×C4—416no—
604C2×C3×C4C2×#4114yes—
605C2×C3×C42−1+414yes—
606C2×C3×C4C2514yes—
607C2×C3×C4C2514yes—
608C2×C3×C4C2514yes—
609C2×C3×C4C2512yes—
610C2×C3×C4C2514yes—
611C2×C3×C4C2512yes—
612C2×C3×C4C2512yes—
613#67—232no—
614#67—232no—
615#67—416no—
616C2×Dic3—22no—
617C2×Dic3—24no—
618C2×Dic3—24no—
619C2×Dic3—28no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—232no—
623C2×Dic3—416no—
624C2×Dic3C2×#4118yes—
625C2×Dic3C2512yes—
626C2×Dic3C2512yes—
627C2×Dic3C2514yes—
628C2×Dic3C2512yes—
629C2×Dic3C2518yes—
630C2×Dic3C2514yes—
631C2×Dic3C2514yes—
632D12—216no—
633D12—28no—
634C4×D3—216no—
635C4×D3—28no—
636C4×D3—216no—
637C4×D3—28no—
638C4×D3—28no—
639C4×D3—216no—
640C4×D3—416no—
641Dic6—216no—
642Dic6—416no—
643Dic6—48no—
644Dic6C2×#41116yescomplemented
645C24—31no—
646C24—32no—
647C24C23×D314yes—
648#41—664no—
649#41—1264no—
650#41—1232no—
651C2×Q8—24no—
652C2×Q8—24no—
653C2×Q8—38no—
654C2×Q8—34no—
655C2×Q8—38no—
656C2×Q8—316no—
657C2×Q8—38no—
658C2×Q8—68no—
659C2×Q8—632no—
660C2×Q8—128no—
661C2×Q8—124no—
662C2×Q8C23×D314yes—
663C2×Q8C23×D314yes—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—316no—
667C2×D4—316no—
668C2×D4—316no—
669C2×D4—34no—
670C2×D4—38no—
671C2×D4—44no—
672C2×D4—68no—
673C2×D4—616no—
674C2×D4—616no—
675C2×D4—64no—
676C2×D4—128no—
677C2×D4C23×D318yes—
678C2×D4C23×D318yes—
679C2×D4C23×D318yes—
680C22×C4—32no—
681C22×C4—316no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—32no—
686C22×C4—34no—
687C22×C4—32no—
688C22×C4—316no—
689C22×C4—34no—
690C22×C4—34no—
691C22×C4—38no—
692C22×C4—38no—
693C22×C4—34no—
694C22×C4—38no—
695C22×C4—316no—
696C22×C4—48no—
697C22×C4—68no—
698C22×C4—68no—
699C22×C4—64no—
700C22×C4—616no—
701C22×C4—64no—
702C22×C4—68no—
703C22×C4—64no—
704C22×C4—128no—
705C22×C4—128no—
706C22×C4C23×D312yes—
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709C22×C4C23×D312yes—
710C22×C4C23×D312yes—
711C22×C4C23×D3116yes—
712C22×C4C23×D311yescharacteristic
713C22×C4C23×D311yescharacteristic
714C4⋊C4—38no—
715C4⋊C4—38no—
716C4⋊C4—316no—
717C4⋊C4—316no—
718C4⋊C4—38no—
719C4⋊C4—38no—
720C4⋊C4—34no—
721C4⋊C4—38no—
722C4⋊C4—38no—
723C4⋊C4—38no—
724C4⋊C4—34no—
725C4⋊C4—38no—
726C4⋊C4—316no—
727C4⋊C4—38no—
728C4⋊C4—316no—
729C4⋊C4C23×D314yes—
730C4⋊C4C23×D318yes—
731C4⋊C4C23×D314yes—
732C4⋊C4C23×D318yes—
733C22⋊C4—316no—
734C22⋊C4—316no—
735C22⋊C4—316no—
736C22⋊C4—38no—
737C22⋊C4—38no—
738C22⋊C4—38no—
739C22⋊C4—38no—
740C22⋊C4—316no—
741C22⋊C4—38no—
742C22⋊C4C23×D3116yes—
743C22⋊C4C23×D3116yes—
744C22⋊C4C23×D3116yes—
745C42—38no—
746C42—34no—
747C42—34no—
748C42—38no—
749C42—34no—
750C42—38no—
751C42—316no—
752C42C23×D318yes—
753C42C23×D314yes—
754C42C23×D318yes—
755C22×C3—28no—
756C22×C3—28no—
757C22×C3—28no—
758C22×C3—416no—
759C22×C3C22×#4112yes—
760C22×C3C2×H(5,𝔽2)12yes—
761C22×C3C2×2−1+412yes—
762C22×C3C2611yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—28no—
766C2×D3—24no—
767C2×D3—24no—
768C2×D3—24no—
769C2×D3—48no—
770C2×D3C2×H(5,𝔽2)14yes—
771C3×C4—24no—
772C3×C4—22no—
773C3×C4—24no—
774C3×C4—24no—
775C3×C4—24no—
776C3×C4C22×#4114yes—
777C3×C4C2×2−1+414yes—
778Dic3—22no—
779Dic3—24no—
780Dic3—24no—
781Dic3—28no—
782Dic3—22no—
783Dic3—22no—
784Dic3C22×#4118yes—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—34no—
789C23—32no—
790C23—34no—
791C23—62no—
792C23—62no—
793C23—64no—
794C23—64no—
795C23—64no—
796C23C24×D318yes—
797C23C24×D311yescharacteristic
798Q8—28no—
799Q8—28no—
800Q8—316no—
801Q8—616no—
802Q8—1216no—
803Q8—128no—
804D4—216no—
805D4—216no—
806D4—48no—
807D4—616no—
808D4—632no—
809D4—632no—
810D4—68no—
811D4—1216no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—38no—
818C2×C4—34no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—34no—
823C2×C4—38no—
824C2×C4—34no—
825C2×C4—416no—
826C2×C4—616no—
827C2×C4—616no—
828C2×C4—68no—
829C2×C4—632no—
830C2×C4—64no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—64no—
835C2×C4—68no—
836C2×C4—68no—
837C2×C4—616no—
838C2×C4—68no—
839C2×C4—1216no—
840C2×C4—1216no—
841C2×C4D3×#4114yes—
842C2×C4#101014yes—
843C2×C4C24×D314yes—
844C2×C4C24×D314yes—
845C2×C4C24×D312yes—
846C2×C4C24×D314yes—
847C2×C4C24×D314yes—
848C2×C4C24×D312yes—
849C2×C4C24×D312yes—
850C2×C3—48no—
851C2×C3#352214yescomplemented
852C2×C3C23×#4111yescharacteristic
853C2×C3C22×H(5,𝔽2)11yescharacteristic
854C2×C3C22×2−1+411yescharacteristic
855D3—24no—
856D3—44no—
857C22—28no—
858C22—28no—
859C22—28no—
860C22—34no—
861C22—416no—
862C22—62no—
863C22—62no—
864C22—68no—
865C22—64no—
866C22—64no—
867C22—64no—
868C22—128no—
869C22C2×D3×#4112yes—
870C22C2×#101012yes—
871C22D3×H(5,𝔽2)12yes—
872C22C25×D311yescharacteristic
873C4—24no—
874C4—24no—
875C4—24no—
876C4—24no—
877C4—22no—
878C4—38no—
879C4—62no—
880C4—64no—
881C4—62no—
882C4—62no—
883C4—64no—
884C4—68no—
885C4C2×D3×#4114yes—
886C4C2×#101014yes—
887C3C2×#352211yescharacteristic, complemented, Sylow
888C2—48no—
889C2—64no—
890C2—124no—
891C2#8705514yesdirect product factor
892C2C22×#101011yescharacteristic
893C2C22×D3×#4111yescharacteristic
894C2C2×D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#559C2
socleC23×C3C25
hypercenterC2×#559D3
hypocenterC3C2×#3522
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×C3×#559C2semidirect
2. #87055C2direct (N × H)
3. C2×#5718C2semidirect
4. C2×#5716C2semidirect
5. C2×#5677C2semidirect
6. C2×#5682C2semidirect
7. C2×#5681C2semidirect
8. C2×#5680C2semidirect
9. C2×#5655C2semidirect
10. C2×#5662C2semidirect
11. C2×#5579C2semidirect
12. C2×#5580C2semidirect
13. C2×C4×D3×Q8C2semidirect
14. C2×Q8×Dic6C2semidirect
15. C2×#5551C2semidirect
16. C2×#5548C2semidirect
17. C2×#5539C2semidirect
18. C2×#5546C2semidirect
24. C3×#559C22semidirect
50. #5718C22semidirect
51. #5716C22semidirect
52. #5682C22semidirect
53. #5681C22semidirect
54. #5680C22semidirect
55. #5677C22semidirect
56. #5662C22semidirect
57. #5655C22semidirect
58. #5580C22semidirect
59. #5579C22semidirect
60. C4×D3×Q8C22semidirect
61. Q8×Dic6C22semidirect
62. #5551C22semidirect
63. #5548C22semidirect
64. #5546C22semidirect
65. #5539C22semidirect
104. C2×#559D3semidirect
259. #559C2×D3semidirect
400. C2×Dic6#41semidirect
644. Dic6C2×#41semidirect
851. C2×C3#3522semidirect
887. C3C2×#3522semidirect
891. C2#87055direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5592
#870552
C2×#57182
C2×#57162
C2×#56772
C2×#56822
C2×#56812
C2×#56802
C2×#56552
C2×#56622
C2×#55792
C2×#55802
C2×C4×D3×Q82
C2×Q8×Dic62
C2×#55512
C2×#55482
C2×#55392
C2×#55462
C2×#35223