Finite Group Databasebeta

← C2×#86774 #11703443

Subgroups — C2×#86774 #11703443

Order 768.

7854 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#550C211yesmaximal, characteristic, complemented
2C2×#5824C212yesmaximal, complemented
3C2×#5832C212yesmaximal, complemented
4#86774C2132yesmaximal, direct product factor
5C2×#5719C212yesmaximal, complemented
6C2×#5718C212yesmaximal, complemented
7C2×#5718C211yesmaximal, characteristic, complemented
8C2×#5716C211yesmaximal, characteristic, complemented
9C2×#5601C214yesmaximal, complemented
10C2×#5599C212yesmaximal, complemented
11C2×#5615C214yesmaximal, complemented
12C2×#5600C212yesmaximal, complemented
13C2×#5580C211yesmaximal, characteristic, complemented
14C2×#5567C211yesmaximal, characteristic, complemented
15C2×#5558C212yesmaximal, complemented
16C2×#5551C211yesmaximal, characteristic, complemented
17C2×#5546C212yesmaximal, complemented
18C2×C4×#237C211yesmaximal, characteristic, complemented
19C2×#3517—31nomaximal, Sylow
20C22×C3×#41C2212yes—
21C22×#237C2211yescharacteristic
22C22×#237C2212yes—
23C22×#237C2212yes—
24C22×#235C2212yes—
25C3×#550C22116yescomplemented
26C2×C3×#127C2211yescharacteristic
27C2×C3×#127C2212yes—
28C2×C3×#121C2212yes—
29C2×C3×#121C2214yes—
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2212yes—
33#5832C22132yescomplemented
34#5824C22132yescomplemented
35C2×#947C2211yescharacteristic
36C2×#946C2211yescharacteristic
37C2×#944C2212yes—
38C2×#940C2214yes—
39C2×#940C2212yes—
40C2×#939C2214yes—
41C2×#939C2214yes—
42C2×#939C2214yes—
43C2×#939C2214yes—
44C2×#939C2214yes—
45C2×#938C2212yes—
46C2×#938C2212yes—
47C2×#938C2212yes—
48C2×#938C2212yes—
49C2×#936C2212yes—
50C2×#935C2214yes—
51C2×#935C2214yes—
52C2×D4×Dic3C2214yes—
53C2×D4×Dic3C2212yes—
54C2×D4×Dic3C2212yes—
55C2×D4×Dic3C2212yes—
56C2×D4×Dic3C2211yescharacteristic
57C2×#929C2214yes—
58C2×C4×#67C2214yes—
59C2×C4×#67C2214yes—
60C2×C4×#67C2212yes—
61C2×#924C2212yes—
62C22×Dic3⋊C4C2214yes—
63C22×C4×Dic3C2212yes—
64#5719C22132yescomplemented
65#5718C22116yescomplemented
66#5718C22132yescomplemented
67#5716C22116yescomplemented
68#5615C22164yescomplemented
69#5601C22164yescomplemented
70#5600C22132yescomplemented
71#5599C22132yescomplemented
72#5580C22116yescomplemented
73#5567C22116yescomplemented
74#5558C22132yescomplemented
75#5551C22116yescomplemented
76#5546C22132yescomplemented
77C4×#237C22116yescomplemented
78C2×#898C2212yes—
79C2×#895C2211yescharacteristic
80C2×#894C2212yes—
81C2×#892C2211yescharacteristic
82C2×D3×C4⋊C4C2212yes—
83C2×#890C2211yescharacteristic
84C2×#889C2214yes—
85C2×#887C2212yes—
86C2×#887C2211yescharacteristic
87C2×#884C2214yes—
88C2×#883C2214yes—
89C2×#67⋊C4C2212yes—
90C2×#67⋊C4C2214yes—
91C2×#879C2214yes—
92C2×#877C2214yes—
93C2×#877C2212yes—
94C2×C4×D12C2211yescharacteristic
95C2×C4×D12C2212yes—
96C2×#872C2212yes—
97C2×C42×D3C2211yescharacteristic
98C2×#870C2212yes—
99C2×#869C2211yescharacteristic
100C2×C4×Dic6C2211yescharacteristic
101C2×C4×Dic6C2212yes—
102#3517—332no—
103C2×#557—31no—
104C2×#553—34no—
105C2×#553—32no—
106C2×#550—31no—
107C2×#550—32no—
108C2×#550—32no—
109C2×#550D311yescharacteristic, complemented
110C2×#547—32no—
111C2×#547—31no—
112C2×#540—32no—
113C2×#540—34no—
114C2×#532—32no—
115C2×#532—31no—
116C2×#529—32no—
117C2×#529—31no—
118C2×#520—32no—
119C2×C4×#41—31no—
120C2×C3×#41—48no—
121C2×C3×#41C23116yes—
122C22×C3×Q8C2311yescharacteristic
123C22×C3×D4C2312yes—
124C22×C3×D4C2311yescharacteristic
125C22×C3×D4C2312yes—
126C22×C3×D4C2314yes—
127C22×C3×D4C2314yes—
128C22×C3×D4C2312yes—
129C23×C3×C4C2312yes—
130C23×C3×C4C2314yes—
131C22×#67C2312yes—
132C22×#67C2314yes—
133C22×#67C2314yes—
134C22×#67C2314yes—
135C22×#67C2314yes—
136C23×Dic3C2312yes—
137C23×Dic3C2314yes—
138C23×Dic3C2314yes—
139C23×Dic3C2312yes—
140C2×#237—28no—
141C2×#237—216no—
142C2×#237—48no—
143C2×#237C2318yes—
144C2×#237C23116yes—
145C2×#237C23116yes—
146C2×#235—48no—
147C2×#235C23116yes—
148C22×D12C2311yescharacteristic
149C22×D12C2312yes—
150C22×C4×D3C2311yescharacteristic
151C22×C4×D3C2311yescharacteristic
152C22×C4×D3C2312yes—
153C22×C4×D3C2314yes—
154C22×C4×D3C2311yescharacteristic
155C22×Dic6C2312yes—
156C22×Dic6C2311yescharacteristic
157C3×#127C2318yes—
158C3×#127C23116yes—
159C3×#121C23116yes—
160C3×#121C23132yes—
161C3×C4×Q8C2318yes—
162C3×C4×D4C2318yes—
163C3×C4×D4C23116yes—
164C2×C3×C4⋊C4C2311yescharacteristic
165C2×C3×C4⋊C4C2311yescharacteristic
166C2×C3×C4⋊C4C2312yes—
167C2×C3×C22⋊C4C2314yes—
168C2×C3×C22⋊C4C2312yes—
169C2×C3×C42C2311yescharacteristic
170C2×C3×C42C2312yes—
171C2×#217C2312yes—
172C2×#217C2314yes—
173C2×#217C2314yes—
174C2×#217C2314yes—
175C2×#217C2314yes—
176#947C2318yes—
177#946C2318yes—
178#944C23116yes—
179#940C23116yes—
180#940C23132yes—
181#939C23132yes—
182#939C23132yes—
183#939C23132yes—
184#939C23132yes—
185#939C23132yes—
186#938C23116yes—
187#938C23116yes—
188#938C23116yes—
189#938C23116yes—
190#936C23116yes—
191#935C23132yes—
192#935C23132yes—
193D4×Dic3C23116yes—
194D4×Dic3C23116yes—
195D4×Dic3C23116yes—
196D4×Dic3C23132yes—
197D4×Dic3C2318yes—
198#929C23132yes—
199C4×#67C23116yes—
200C4×#67C23132yes—
201C4×#67C23132yes—
202C2×(C2×D3)⋊C4C2312yes—
203C2×(C2×D3)⋊C4C2312yes—
204C2×(C2×D3)⋊C4C2312yes—
205C2×(C2×D3)⋊C4C2312yes—
206C2×(C2×D3)⋊C4C2312yes—
207C2×(C2×D3)⋊C4C2312yes—
208C2×C4⋊Dic3C2312yes—
209C2×C4⋊Dic3C2311yescharacteristic
210C2×C4⋊Dic3C2312yes—
211C2×C4⋊Dic3C2312yes—
212C2×C4⋊Dic3C2311yescharacteristic
213#924C23116yes—
214C2×Dic3⋊C4C2312yes—
215C2×Dic3⋊C4C2314yes—
216C2×Dic3⋊C4C2314yes—
217C2×Dic3⋊C4C2314yes—
218C2×Dic3⋊C4C2312yes—
219C2×Dic3⋊C4C2312yes—
220C2×Dic3⋊C4C2314yes—
221C2×Dic3⋊C4C2312yes—
222C2×Dic3⋊C4C23132yes—
223C2×C4×Dic3C2314yes—
224C2×C4×Dic3C2312yes—
225C2×C4×Dic3C2311yescharacteristic
226C2×C4×Dic3C2311yescharacteristic
227C2×C4×Dic3C2311yescharacteristic
228C2×C4×Dic3C2312yes—
229C2×C4×Dic3C2312yes—
230C2×C4×Dic3C23116yes—
231#898C23116yes—
232#895C2318yes—
233#894C23116yes—
234#892C2318yes—
235D3×C4⋊C4C23116yes—
236#890C2318yes—
237#889C23132yes—
238#887C2318yes—
239#887C23116yes—
240#884C23132yes—
241#883C23132yes—
242#67⋊C4C23116yes—
243#67⋊C4C23132yes—
244#879C23132yes—
245#877C23116yes—
246#877C23132yes—
247C4×D12C2318yes—
248C4×D12C23116yes—
249#872C23116yes—
250C42×D3C2318yes—
251#870C23116yes—
252#869C2318yes—
253C4×Dic6C2318yes—
254C4×Dic6C23116yes—
255C22×#41—31no—
256C22×#41—32no—
257C22×#41—32no—
258C22×#41—32no—
259C22×#41C2×D312yes—
260#557—316no—
261#553—364no—
262#553—332no—
263#550—316no—
264#550—332no—
265#550—332no—
266#550C2×D3116yescomplemented
267#547—332no—
268#547—316no—
269#540—332no—
270#540—364no—
271#532—332no—
272#532—316no—
273C2×C4⋊Q8—32no—
274C2×C4⋊Q8—31no—
275C2×#127—32no—
276C2×#127—34no—
277C2×#127C2×D311yescharacteristic
278C2×#127C2×D312yes—
279#529—332no—
280#529—316no—
281C2×#126—32no—
282C2×#126—34no—
283C2×#125—31no—
284C2×#125—34no—
285C2×#125—32no—
286C2×#124—31no—
287C2×#124—32no—
288C2×#123—34no—
289C2×#123—34no—
290C2×#123—34no—
291C2×#123—32no—
292C2×#123—34no—
293C2×C22⋊Q8—31no—
294C2×C22⋊Q8—32no—
295C2×#121—32no—
296C2×#121—34no—
297C2×#121—32no—
298C2×#121—34no—
299C2×#121—32no—
300C2×#121—34no—
301C2×#121—32no—
302C2×#121—34no—
303C2×#121—34no—
304C2×#121—31no—
305C2×#121—34no—
306C2×#121C2×D312yes—
307C2×#121C2×D314yes—
308#520—332no—
309C4×#41—316no—
310C2×C4×Q8—31no—
311C2×C4×Q8—32no—
312C2×C4×Q8—31no—
313C2×C4×Q8—32no—
314C2×C4×Q8C2×D311yescharacteristic
315C2×C4×D4—31no—
316C2×C4×D4—32no—
317C2×C4×D4—32no—
318C2×C4×D4—34no—
319C2×C4×D4—32no—
320C2×C4×D4—32no—
321C2×C4×D4—34no—
322C2×C4×D4—34no—
323C2×C4×D4—32no—
324C2×C4×D4—34no—
325C2×C4×D4—31no—
326C2×C4×D4—32no—
327C2×C4×D4C2×D311yescharacteristic
328C2×C4×D4C2×D312yes—
329C2×#117—31no—
330C2×#117—32no—
331C2×#117—34no—
332C2×#117—32no—
333C22×C4⋊C4—34no—
334C22×C4⋊C4—32no—
335C22×C42—32no—
336C22×C42—31no—
337C24×C3C2414yes—
338C24×C3C2412yes—
339C23×D3C2411yescharacteristic
340C23×D3C2412yes—
341C3×#41—432no—
342C2×C3×Q8—24no—
343C2×C3×Q8C2414yes—
344C2×C3×D4—24no—
345C2×C3×D4—28no—
346C2×C3×D4—28no—
347C2×C3×D4—44no—
348C2×C3×D4—48no—
349C2×C3×D4—48no—
350C2×C3×D4C2418yes—
351C2×C3×D4C2418yes—
352C2×C3×D4C2414yes—
353C2×C3×D4C24116yes—
354C2×C3×D4C2418yes—
355C2×C3×D4C24116yes—
356C22×C3×C4—28no—
357C22×C3×C4—48no—
358C22×C3×C4C2412yes—
359C22×C3×C4C2412yes—
360C22×C3×C4C2418yes—
361C22×C3×C4C2411yescharacteristic
362C22×C3×C4C2412yes—
363C22×C3×C4C24116yes—
364C22×C3×C4C2411yescharacteristic
365C22×C3×C4C2411yescharacteristic
366C2×#67—28no—
367C2×#67—216no—
368C2×#67—48no—
369C2×#67—48no—
370C2×#67—48no—
371C2×#67C2418yes—
372C2×#67C24116yes—
373C2×#67C24116yes—
374C2×#67C24116yes—
375C2×#67C24116yes—
376C22×Dic3—28no—
377C22×Dic3—216no—
378C22×Dic3—48no—
379C22×Dic3—44no—
380C22×Dic3C2418yes—
381C22×Dic3C24116yes—
382C22×Dic3C2411yescharacteristic
383C22×Dic3C2411yescharacteristic
384C22×Dic3C2412yes—
385C22×Dic3C2411yescharacteristic
386C22×Dic3C2414yes—
387C22×Dic3C2412yes—
388C22×Dic3C2418yes—
389C22×Dic3C24116yes—
390C22×Dic3C2412yes—
391#237—232no—
392#237—264no—
393#237—432no—
394#235—432no—
395C2×D12—24no—
396C2×D12—44no—
397C2×D12C2414yes—
398C2×D12C2418yes—
399C2×C4×D3—24no—
400C2×C4×D3—28no—
401C2×C4×D3—24no—
402C2×C4×D3—42no—
403C2×C4×D3—48no—
404C2×C4×D3C2414yes—
405C2×C4×D3C2414yes—
406C2×C4×D3C2418yes—
407C2×C4×D3C2414yes—
408C2×C4×D3C24116yes—
409C2×Dic6—28no—
410C2×Dic6#4118yescomplemented
411C2×Dic6C2418yes—
412C2×Dic6C2414yes—
413C3×C4⋊C4C2414yes—
414C3×C4⋊C4C2414yes—
415C3×C4⋊C4C2418yes—
416C3×C22⋊C4C24116yes—
417C3×C22⋊C4C2418yes—
418C3×C42C2414yes—
419C3×C42C2418yes—
420#217C2418yes—
421#217C24116yes—
422#217C24116yes—
423#217C24116yes—
424#217C24116yes—
425(C2×D3)⋊C4C2418yes—
426(C2×D3)⋊C4C2418yes—
427(C2×D3)⋊C4C2418yes—
428(C2×D3)⋊C4C2418yes—
429(C2×D3)⋊C4C2418yes—
430(C2×D3)⋊C4C2418yes—
431C4⋊Dic3C2418yes—
432C4⋊Dic3C2414yes—
433C4⋊Dic3C2418yes—
434C4⋊Dic3C2418yes—
435C4⋊Dic3C2414yes—
436Dic3⋊C4C2418yes—
437Dic3⋊C4C24116yes—
438Dic3⋊C4C24116yes—
439Dic3⋊C4C24116yes—
440Dic3⋊C4C2418yes—
441Dic3⋊C4C2418yes—
442Dic3⋊C4C24116yes—
443Dic3⋊C4C2418yes—
444C4×Dic3C24116yes—
445C4×Dic3C2418yes—
446C4×Dic3C2414yes—
447C4×Dic3C2414yes—
448C4×Dic3C2414yes—
449C4×Dic3C2418yes—
450C4×Dic3C2418yes—
451C2×#41—38no—
452C2×#41—316no—
453C2×#41—316no—
454C2×#41—316no—
455C2×#41—48no—
456C2×#41—68no—
457C2×#41—616no—
458C2×#41—128no—
459C2×#41—128no—
460C2×#41C22×D3116yes—
461C22×Q8—31no—
462C22×Q8—32no—
463C22×Q8C22×D311yescharacteristic
464C22×D4—32no—
465C22×D4—34no—
466C22×D4—34no—
467C22×D4—34no—
468C22×D4—34no—
469C22×D4—31no—
470C22×D4—32no—
471C22×D4C22×D311yescharacteristic
472C22×D4C22×D312yes—
473C22×D4C22×D312yes—
474C22×D4C22×D312yes—
475C22×D4C22×D314yes—
476C22×D4C22×D314yes—
477C23×C4—34no—
478C23×C4—32no—
479C23×C4—34no—
480C23×C4—32no—
481C23×C4—32no—
482C23×C4—31no—
483C23×C4—31no—
484C23×C4—34no—
485C23×C4—31no—
486C23×C4C22×D312yes—
487C23×C4C22×D314yes—
488C4⋊Q8—316no—
489C4⋊Q8—38no—
490#127—316no—
491#127—332no—
492#127C22×D318yes—
493#127C22×D3116yes—
494#126—316no—
495#126—332no—
496#125—38no—
497#125—332no—
498#125—316no—
499#124—38no—
500#124—316no—
501#123—332no—
502#123—332no—
503#123—332no—
504#123—316no—
505#123—332no—
506C22⋊Q8—38no—
507C22⋊Q8—316no—
508#121—316no—
509#121—332no—
510#121—316no—
511#121—332no—
512#121—316no—
513#121—332no—
514#121—316no—
515#121—332no—
516#121—332no—
517#121—38no—
518#121—332no—
519#121C22×D3116yes—
520#121C22×D3132yes—
521C4×Q8—38no—
522C4×Q8—316no—
523C4×Q8—38no—
524C4×Q8—316no—
525C4×Q8C22×D318yes—
526C4×D4—38no—
527C4×D4—316no—
528C4×D4—316no—
529C4×D4—332no—
530C4×D4—316no—
531C4×D4—316no—
532C4×D4—332no—
533C4×D4—332no—
534C4×D4—316no—
535C4×D4—332no—
536C4×D4—38no—
537C4×D4—316no—
538C4×D4C22×D318yes—
539C4×D4C22×D3116yes—
540#117—38no—
541#117—316no—
542#117—332no—
543#117—316no—
544C2×C4⋊C4—32no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—34no—
547C2×C4⋊C4—34no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—332no—
550C2×C4⋊C4—32no—
551C2×C4⋊C4—32no—
552C2×C4⋊C4—31no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—32no—
555C2×C4⋊C4—34no—
556C2×C4⋊C4—32no—
557C2×C4⋊C4—34no—
558C2×C4⋊C4—316no—
559C2×C4⋊C4C22×D311yescharacteristic
560C2×C4⋊C4C22×D311yescharacteristic
561C2×C4⋊C4C22×D312yes—
562C2×C22⋊C4—32no—
563C2×C22⋊C4—34no—
564C2×C22⋊C4—34no—
565C2×C22⋊C4—34no—
566C2×C22⋊C4—34no—
567C2×C22⋊C4—32no—
568C2×C22⋊C4—32no—
569C2×C22⋊C4—32no—
570C2×C22⋊C4—32no—
571C2×C22⋊C4—32no—
572C2×C22⋊C4—32no—
573C2×C22⋊C4C22×D314yes—
574C2×C22⋊C4C22×D312yes—
575C2×C42—32no—
576C2×C42—31no—
577C2×C42—32no—
578C2×C42—31no—
579C2×C42—34no—
580C2×C42—32no—
581C2×C42—316no—
582C2×C42—31no—
583C2×C42—38no—
584C2×C42C22×D312yes—
585C2×C42C22×D311yescharacteristic
586C23×C3—28no—
587C23×C3—24no—
588C23×C3—28no—
589C23×C3—24no—
590C23×C3—24no—
591C23×C3—28no—
592C23×C3C2518yes—
593C23×C3C2514yes—
594C23×C3C2511yescharacteristic
595C22×D3—22no—
596C22×D3—24no—
597C22×D3—22no—
598C22×D3—24no—
599C22×D3—22no—
600C22×D3—24no—
601C22×D3C2512yes—
602C22×D3C2514yes—
603C3×Q8—28no—
604C3×D4—28no—
605C3×D4—216no—
606C3×D4—216no—
607C3×D4—48no—
608C3×D4—416no—
609C3×D4—416no—
610C2×C3×C4—24no—
611C2×C3×C4—24no—
612C2×C3×C4—22no—
613C2×C3×C4—24no—
614C2×C3×C4—216no—
615C2×C3×C4—416no—
616C2×C3×C4C2×#4114yes—
617C2×C3×C4H(5,𝔽2)14yes—
618C2×C3×C4C2514yes—
619C2×C3×C4C2514yes—
620C2×C3×C4C2512yes—
621C2×C3×C4C2514yes—
622C2×C3×C4C2512yes—
623C2×C3×C4C2512yes—
624#67—216no—
625#67—232no—
626#67—416no—
627#67—416no—
628#67—416no—
629C2×Dic3—22no—
630C2×Dic3—24no—
631C2×Dic3—28no—
632C2×Dic3—22no—
633C2×Dic3—22no—
634C2×Dic3—24no—
635C2×Dic3—216no—
636C2×Dic3—232no—
637C2×Dic3—416no—
638C2×Dic3—48no—
639C2×Dic3C2×#4118yes—
640C2×Dic3C2512yes—
641C2×Dic3C2512yes—
642C2×Dic3C2514yes—
643C2×Dic3C2512yes—
644C2×Dic3C2518yes—
645C2×Dic3C2514yes—
646C2×Dic3C2514yes—
647D12—28no—
648D12—48no—
649C4×D3—28no—
650C4×D3—216no—
651C4×D3—28no—
652C4×D3—44no—
653C4×D3—416no—
654Dic6—216no—
655Dic6C2×#41116yescomplemented
656C24—31no—
657C24—32no—
658C24C23×D312yes—
659C24C23×D314yes—
660#41—432no—
661#41—632no—
662#41—664no—
663#41—1232no—
664#41—1232no—
665C2×Q8—24no—
666C2×Q8—38no—
667C2×Q8—34no—
668C2×Q8—38no—
669C2×Q8—68no—
670C2×Q8C23×D314yes—
671C2×D4—28no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—38no—
675C2×D4—316no—
676C2×D4—316no—
677C2×D4—316no—
678C2×D4—316no—
679C2×D4—34no—
680C2×D4—38no—
681C2×D4—48no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—68no—
685C2×D4—616no—
686C2×D4—64no—
687C2×D4—124no—
688C2×D4—128no—
689C2×D4—128no—
690C2×D4—128no—
691C2×D4C23×D314yes—
692C2×D4C23×D318yes—
693C2×D4C23×D318yes—
694C2×D4C23×D318yes—
695C2×D4C23×D3116yes—
696C2×D4C23×D3116yes—
697C22×C4—28no—
698C22×C4—32no—
699C22×C4—38no—
700C22×C4—316no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—32no—
704C22×C4—31no—
705C22×C4—34no—
706C22×C4—32no—
707C22×C4—38no—
708C22×C4—316no—
709C22×C4—34no—
710C22×C4—34no—
711C22×C4—38no—
712C22×C4—34no—
713C22×C4—316no—
714C22×C4—48no—
715C22×C4—616no—
716C22×C4—68no—
717C22×C4—64no—
718C22×C4—68no—
719C22×C4—64no—
720C22×C4—128no—
721C22×C4—122no—
722C22×C4—128no—
723C22×C4—124no—
724C22×C4C23×D318yes—
725C22×C4C23×D312yes—
726C22×C4C23×D312yes—
727C22×C4C23×D311yescharacteristic
728C22×C4C23×D312yes—
729C22×C4C23×D3116yes—
730C22×C4C23×D311yescharacteristic
731C22×C4C23×D311yescharacteristic
732C4⋊C4—38no—
733C4⋊C4—38no—
734C4⋊C4—316no—
735C4⋊C4—316no—
736C4⋊C4—38no—
737C4⋊C4—38no—
738C4⋊C4—38no—
739C4⋊C4—34no—
740C4⋊C4—34no—
741C4⋊C4—38no—
742C4⋊C4—316no—
743C4⋊C4—38no—
744C4⋊C4—316no—
745C4⋊C4C23×D314yes—
746C4⋊C4C23×D314yes—
747C4⋊C4C23×D318yes—
748C22⋊C4—38no—
749C22⋊C4—316no—
750C22⋊C4—316no—
751C22⋊C4—316no—
752C22⋊C4—316no—
753C22⋊C4—38no—
754C22⋊C4—38no—
755C22⋊C4—38no—
756C22⋊C4—38no—
757C22⋊C4—38no—
758C22⋊C4—38no—
759C22⋊C4C23×D3116yes—
760C22⋊C4C23×D318yes—
761C42—34no—
762C42—38no—
763C42—34no—
764C42—38no—
765C42—34no—
766C42—38no—
767C42—316no—
768C42C23×D314yes—
769C42C23×D318yes—
770C22×C3—28no—
771C22×C3—24no—
772C22×C3—28no—
773C22×C3—24no—
774C22×C3—24no—
775C22×C3—28no—
776C22×C3—416no—
777C22×C3—48no—
778C22×C3C22×#4112yes—
779C22×C3C2×H(5,𝔽2)12yes—
780C22×C3#58512yes—
781C22×C3C2611yescharacteristic
782C2×D3—22no—
783C2×D3—24no—
784C2×D3—22no—
785C2×D3—24no—
786C2×D3—22no—
787C2×D3—24no—
788C2×D3—44no—
789C2×D3—48no—
790C3×C4—24no—
791C3×C4—24no—
792C3×C4—22no—
793C3×C4—24no—
794C3×C4C22×#4114yes—
795C3×C4C2×H(5,𝔽2)14yes—
796Dic3—22no—
797Dic3—24no—
798Dic3—28no—
799Dic3—22no—
800Dic3—22no—
801Dic3—24no—
802Dic3C22×#4118yes—
803C23—24no—
804C23—28no—
805C23—24no—
806C23—28no—
807C23—24no—
808C23—28no—
809C23—32no—
810C23—34no—
811C23—62no—
812C23—64no—
813C23—62no—
814C23—64no—
815C23—62no—
816C23—64no—
817C23C24×D314yes—
818C23C24×D318yes—
819C23C24×D311yescharacteristic
820Q8—28no—
821Q8—316no—
822Q8—616no—
823D4—216no—
824D4—28no—
825D4—216no—
826D4—416no—
827D4—48no—
828D4—416no—
829D4—616no—
830D4—632no—
831D4—68no—
832D4—128no—
833D4—1216no—
834D4—1216no—
835D4—1216no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—24no—
840C2×C4—216no—
841C2×C4—38no—
842C2×C4—34no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—34no—
846C2×C4—32no—
847C2×C4—38no—
848C2×C4—34no—
849C2×C4—416no—
850C2×C4—616no—
851C2×C4—632no—
852C2×C4—62no—
853C2×C4—68no—
854C2×C4—62no—
855C2×C4—64no—
856C2×C4—62no—
857C2×C4—64no—
858C2×C4—68no—
859C2×C4—68no—
860C2×C4—616no—
861C2×C4—1216no—
862C2×C4—124no—
863C2×C4—1216no—
864C2×C4—128no—
865C2×C4#100414yes—
866C2×C4D3×#4114yes—
867C2×C4C24×D314yes—
868C2×C4C24×D314yes—
869C2×C4C24×D312yes—
870C2×C4C24×D314yes—
871C2×C4C24×D312yes—
872C2×C4C24×D312yes—
873C2×C3—48no—
874C2×C3—44no—
875C2×C3#351714yescomplemented
876C2×C3C23×#4111yescharacteristic
877C2×C3C22×H(5,𝔽2)11yescharacteristic
878C2×C3C2×#58511yescharacteristic
879D3—42no—
880D3—44no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—48no—
888C22—416no—
889C22—62no—
890C22—64no—
891C22—62no—
892C22—64no—
893C22—62no—
894C22—64no—
895C22—124no—
896C22—128no—
897C22C2×#100412yes—
898C22C2×D3×#4112yes—
899C22#596612yes—
900C22C25×D311yescharacteristic
901C4—24no—
902C4—24no—
903C4—22no—
904C4—24no—
905C4—38no—
906C4—62no—
907C4—68no—
908C4—62no—
909C4—64no—
910C4—62no—
911C4—64no—
912C4C2×#100414yes—
913C4C2×D3×#4114yes—
914C3C2×#351711yescharacteristic, complemented, Sylow
915C2—44no—
916C2—48no—
917C2—122no—
918C2—124no—
919C2#8677414yesdirect product factor
920C2C22×#100411yescharacteristic
921C2C22×D3×#4111yescharacteristic
922C2C2×#596611yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#550C2
socleC23×C3C25
hypercenterC2×#550D3
hypocenterC3C2×#3517
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×C3×#550C2semidirect
2. C2×#5824C2semidirect
3. C2×#5832C2semidirect
4. #86774C2direct (N × H)
5. C2×#5719C2semidirect
6. C2×#5718C2semidirect
7. C2×#5718C2semidirect
8. C2×#5716C2semidirect
9. C2×#5601C2semidirect
10. C2×#5599C2semidirect
11. C2×#5615C2semidirect
12. C2×#5600C2semidirect
13. C2×#5580C2semidirect
14. C2×#5567C2semidirect
15. C2×#5558C2semidirect
16. C2×#5551C2semidirect
17. C2×#5546C2semidirect
18. C2×C4×#237C2semidirect
25. C3×#550C22semidirect
33. #5832C22semidirect
34. #5824C22semidirect
64. #5719C22semidirect
65. #5718C22semidirect
66. #5718C22semidirect
67. #5716C22semidirect
68. #5615C22semidirect
69. #5601C22semidirect
70. #5600C22semidirect
71. #5599C22semidirect
72. #5580C22semidirect
73. #5567C22semidirect
74. #5558C22semidirect
75. #5551C22semidirect
76. #5546C22semidirect
77. C4×#237C22semidirect
109. C2×#550D3semidirect
266. #550C2×D3semidirect
410. C2×Dic6#41semidirect
655. Dic6C2×#41semidirect
875. C2×C3#3517semidirect
914. C3C2×#3517semidirect
919. C2#86774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5502
C2×#58242
C2×#58322
#867742
C2×#57192
C2×#57182
C2×#57162
C2×#56012
C2×#55992
C2×#56152
C2×#56002
C2×#55802
C2×#55672
C2×#55582
C2×#55512
C2×#55462
C2×C4×#2372
C2×#35173