Finite Group Databasebeta

← D3×#5574 #11900106

Subgroups — D3×#5574 #11900106

Order 1152.

3427 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2#10596045C211yesmaximal, characteristic, complemented
3C3×#5574C211yesmaximal, characteristic, complemented
4C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
5#10595394C211yesmaximal, characteristic, complemented
6D3×Q8×Dic3C211yesmaximal, characteristic, complemented
7#10595353C211yesmaximal, characteristic, complemented
8D3×#893C213yesmaximal, complemented
9D32×C4⋊C4C213yesmaximal, complemented
10#10594361C213yesmaximal, complemented
11#10594327C213yesmaximal, complemented
12C4×D3×D12C213yesmaximal, complemented
13D3×#872C213yesmaximal, complemented
14#10593890C213yesmaximal, complemented
15#10593889C213yesmaximal, complemented
16D3×#520—31nomaximal
17C2×#5574—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21D3×#239C4116yescomplemented
22C2×D3×D12C2213yes—
23C2×C4×D32C2216yes—
24C2×C4×D32C2213yes—
25C2×#3799C2213yes—
26C2×#3796C2213yes—
27C32×C4×Q8C2211yescharacteristic, complemented
28Q8×C3⋊Dic3C2211yescharacteristic, complemented
29#64102C2213yescomplemented
30C4⋊C4×C3⋊D3C2213yescomplemented
31C4×C4⋊(C3⋊D3)C2213yescomplemented
32#64081C2213yescomplemented
33C3×Q8×Dic3C2211yescharacteristic, complemented
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×#893C2213yescomplemented
36C3×D3×C4⋊C4C2213yes—
37C3×D3×C4⋊C4C2213yescomplemented
38C3×#887C2213yescomplemented
39C3×C4×D12C2213yescomplemented
40C3×#872C2213yescomplemented
41C3×C42×D3C2213yes—
42C3×C4×Dic6C2213yescomplemented
43D3×(C2×D3)⋊C4C2213yes—
44D3×(C2×D3)⋊C4C2213yes—
45#63904C2216yescomplemented
46C4×#626C2216yescomplemented
47#63900C2213yescomplemented
48#63898C2213yescomplemented
49#63894C2213yescomplemented
50#63894C2213yescomplemented
51Dic3×D12C2213yescomplemented
52D3×C4⋊Dic3C2213yes—
53D3×C4⋊Dic3C2213yescomplemented
54#63883C2216yescomplemented
55#63881C2216yescomplemented
56#63880C2216yescomplemented
57#63877C2213yescomplemented
58#63877C2213yescomplemented
59D3×Dic3⋊C4C2213yes—
60D3×Dic3⋊C4C2211yescharacteristic
61D3×Dic3⋊C4C2216yescomplemented
62C4×D3×Dic3C2213yes—
63#63874C2213yescomplemented
64#63855C2213yescomplemented
65#63843C2213yescomplemented
66Dic3×Dic6C2213yescomplemented
67#63836C2213yescomplemented
68#63836C2213yescomplemented
69C2×D3×#41—31no—
70C22×#239—31no—
71C3×#520—31no—
72C2×C3×C4×Q8—31no—
73#5827—31no—
74C2×Q8×Dic3—31no—
75#5574—31no—
76#5574—31no—
77#5574—31no—
78#5574—31no—
79#5574—31no—
80#5574—33no—
81#5574—33no—
82#5574—33no—
83#5574—33no—
84#5574—61no—
85#5574D311yescharacteristic, direct product factor
86C4×D3×Q8—31no—
87C4×D3×Q8D311yescharacteristic, complemented
88#5546—33no—
89#5546—33no—
90C4×D3×D4—33no—
91C4×D3×D4—33no—
92#5523—33no—
93D3×#117—33no—
94#5504—33no—
95C2×#893—33no—
96C2×D3×C4⋊C4—33no—
97C2×D3×C4⋊C4—33no—
98C2×C4×D12—33no—
99C2×#872—33no—
100C22×D32C2313yes—
101C2×C32×Q8C2311yescharacteristic
102#3832C2×C418yescomplemented
103C2×C4⋊(C3⋊D3)C2313yes—
104C2×C4×C3⋊D3C2316yes—
105C2×C4×C3⋊D3C2313yes—
106C3×#239C2×C418yescomplemented
107C3×D3×Q8C2×C418yescomplemented
108C2×C3×D12C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2316yes—
112C2×C3×C4×D3C2313yes—
113C2×C3×C4×D3C2313yes—
114C2×C3×Dic6C2313yes—
115C2×#626C2316yes—
116C2×#624C2316yes—
117C2×#624C2313yes—
118C2×D3×Dic3C2313yes—
119C2×D3×Dic3C2311yescharacteristic
120C2×D3×Dic3C2316yes—
121C2×D3×Dic3C2311yescharacteristic
122C2×D3×Dic3C2313yes—
123D3×D12C2×C4124yescomplemented
124C4×D32—412no—
125C4×D32C2×C4124yescomplemented
126#3799C2×C4124yescomplemented
127#3796C2×C4124yescomplemented
128C32×C4⋊C4C2313yes—
129C32×C42C2313yes—
130#3752C2313yes—
131#3752C2313yes—
132C4⋊(C3⋊Dic3)C2313yes—
133#3750C2311yescharacteristic
134#3750C2313yes—
135C4×C3⋊Dic3C2313yes—
136C3×(C2×D3)⋊C4C2313yes—
137C3×(C2×D3)⋊C4C2313yes—
138C3×C4⋊Dic3C2313yes—
139C3×C4⋊Dic3C2313yes—
140C3×Dic3⋊C4C2316yes—
141C3×Dic3⋊C4C2313yes—
142C3×Dic3⋊C4C2311yescharacteristic
143C3×C4×Dic3C2313yes—
144C3×C4×Dic3C2313yes—
145C3×C4×Dic3C2313yes—
146C3×C4×Dic3C2313yes—
147#3724C2311yescharacteristic
148#3724C2313yes—
149Dic3⋊Dic3C2311yescharacteristic
150Dic3⋊Dic3C2313yes—
151Dic3⋊Dic3C2316yes—
152#3722C2313yes—
153#3722C2313yes—
154(C2×D3)⋊Dic3C2313yes—
155(C2×D3)⋊Dic3C2313yes—
156Dic32C2313yes—
157Dic32C2313yes—
158C2×#520—91noSylow
159C2×C3×#41—31no—
160C22×C3×Q8—31no—
161D3×#41—316no—
162C2×#239—31no—
163C2×#239—31no—
164C2×#239—316no—
165C2×#239—33no—
166C2×#239—33no—
167C2×#239—61no—
168C2×#239C2×D311yescharacteristic
169C2×D3×Q8C2×D311yescharacteristic
170C2×#237—33no—
171C2×D3×D4—33no—
172C2×#235—33no—
173C22×D12—33no—
174C22×C4×D3—33no—
175C22×C4×D3—33no—
176C22×C4×D3—36no—
177C22×C4×D3—36no—
178C3×C4×Q8—21no—
179C3×C4×Q8—31no—
180C3×C4×Q8—31no—
181C3×C4×Q8—33no—
182C3×C4×Q8—33no—
183C3×C4×Q8C2×D311yescharacteristic, complemented
184C3×C4×Q8C2×D311yescharacteristic, complemented
185C3×C4×D4—33no—
186C3×C4×D4—33no—
187C3×#117—33no—
188C2×C3×C4⋊C4—33no—
189C2×C3×C4⋊C4—33no—
190C2×C3×C42—33no—
191Q8×Dic3—31no—
192Q8×Dic3—31no—
193Q8×Dic3—33no—
194Q8×Dic3—33no—
195Q8×Dic3—61no—
196Q8×Dic3C2×D311yescharacteristic, complemented
197Q8×Dic3C2×D311yescharacteristic, complemented
198D4×Dic3—33no—
199D4×Dic3—33no—
200C4×#67—36no—
201C4×#67—36no—
202C2×(C2×D3)⋊C4—33no—
203C2×(C2×D3)⋊C4—33no—
204#926—33no—
205C2×C4⋊Dic3—33no—
206C2×C4⋊Dic3—33no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—33no—
209C2×Dic3⋊C4—36no—
210C2×C4×Dic3—33no—
211#893—33no—
212#893—36no—
213#893—33no—
214#893—33no—
215#893—36no—
216#893—33no—
217#893—33no—
218#893—63no—
219#893C2×D313yescomplemented
220#892—33no—
221#892—33no—
222D3×C4⋊C4—33no—
223D3×C4⋊C4—36no—
224D3×C4⋊C4—33no—
225D3×C4⋊C4—33no—
226D3×C4⋊C4—31no—
227D3×C4⋊C4—33no—
228D3×C4⋊C4—33no—
229D3×C4⋊C4—33no—
230D3×C4⋊C4—33no—
231D3×C4⋊C4—36no—
232D3×C4⋊C4—36no—
233D3×C4⋊C4—63no—
234D3×C4⋊C4C2×D313yes—
235D3×C4⋊C4C2×D313yescomplemented
236#887—33no—
237#887C2×D313yescomplemented
238#67⋊C4—36no—
239#67⋊C4—36no—
240D3×C22⋊C4—33no—
241D3×C22⋊C4—33no—
242#877—33no—
243#877—33no—
244C4×D12—33no—
245C4×D12—36no—
246C4×D12—33no—
247C4×D12—33no—
248C4×D12—36no—
249C4×D12—33no—
250C4×D12—33no—
251C4×D12—63no—
252C4×D12C2×D313yescomplemented
253#872—33no—
254#872—33no—
255#872—33no—
256#872—33no—
257#872—33no—
258#872—33no—
259#872—33no—
260#872—33no—
261#872—33no—
262#872—63no—
263#872C2×D313yescomplemented
264C42×D3—33no—
265C42×D3C2×D313yes—
266C4×Dic6—33no—
267C4×Dic6C2×D313yescomplemented
268C22×C3⋊D3C2413yes—
269C22×C3×D3C2413yes—
270C22×C3×D3C2411yescharacteristic
271C2×D32—26no—
272C2×D32—26no—
273C2×D32C22×C4112yes—
274C32×Q8C22×C414yescomplemented
275C2×C32×C4C2411yescharacteristic
276C2×C32×C4C2413yes—
277C2×C32×C4C2413yes—
278C2×C3⋊Dic3C2411yescharacteristic
279C2×C3⋊Dic3C2413yes—
280C2×C3⋊Dic3C2411yescharacteristic
281C4⋊(C3⋊D3)C22×C4112yescomplemented
282C4×C3⋊D3—46no—
283C4×C3⋊D3C22×C4112yescomplemented
284C2×C3×Dic3C2411yescharacteristic
285C2×C3×Dic3C2413yes—
286C2×C3×Dic3C2411yescharacteristic
287C2×C3×Dic3C2413yes—
288C2×C3×Dic3C2413yes—
289C2×C3×Dic3C2411yescharacteristic
290C3×D12C22×C4112yescomplemented
291C3×C4×D3—26no—
292C3×C4×D3—22no—
293C3×C4×D3—46no—
294C3×C4×D3C22×C4112yes—
295C3×C4×D3C22×C4112yescomplemented
296C3×Dic6C22×C4112yescomplemented
297#626C22×C4124yescomplemented
298#624—46no—
299#624C22×C4112yescomplemented
300D3×Dic3—26no—
301D3×Dic3—22no—
302D3×Dic3—46no—
303D3×Dic3C22×C414yes—
304D3×Dic3C22×C4112yescomplemented
305C22×#41—91no—
306#520—31no—
307#520—93no—
308#520—93no—
309#520—93no—
310#520—93no—
311#520—91no—
312#520—91no—
313#520—91no—
314C2×C4×Q8—31no—
315C2×C4×Q8—91no—
316C2×C4×D4—93no—
317C2×C4×D4—93no—
318C2×#117—93no—
319C22×C4⋊C4—93no—
320C23×D3—33no—
321C23×D3—33no—
322C3×#41—38no—
323C2×C3×Q8—21no—
324C2×C3×Q8—38no—
325C2×C3×Q8—33no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×D4—33no—
329C22×C3×C4—33no—
330C22×C3×C4—33no—
331C22×C3×C4—31no—
332C22×C3×C4—33no—
333C22×C3×C4—36no—
334C2×#67—36no—
335C22×Dic3—33no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—33no—
339C22×Dic3—36no—
340#239—38no—
341#239—38no—
342#239—324no—
343#239—324no—
344#239—68no—
345#239C4×D318yescomplemented
346D3×Q8C4×D318yescomplemented
347#237—324no—
348D3×D4—324no—
349#235—324no—
350C2×D12—36no—
351C2×D12—33no—
352C2×D12—33no—
353C2×D12—324no—
354C2×D12—63no—
355C2×D12C22×D313yes—
356C2×C4×D3—33no—
357C2×C4×D3—31no—
358C2×C4×D3—33no—
359C2×C4×D3—33no—
360C2×C4×D3—33no—
361C2×C4×D3—33no—
362C2×C4×D3—324no—
363C2×C4×D3—324no—
364C2×C4×D3—31no—
365C2×C4×D3—33no—
366C2×C4×D3—36no—
367C2×C4×D3—36no—
368C2×C4×D3—36no—
369C2×C4×D3—36no—
370C2×C4×D3—36no—
371C2×C4×D3—63no—
372C2×C4×D3—66no—
373C2×C4×D3—1212no—
374C2×C4×D3—1212no—
375C2×C4×D3C22×D311yescharacteristic
376C2×C4×D3C22×D313yes—
377C2×C4×D3C22×D316yes—
378C2×C4×D3C22×D313yes—
379C2×C4×D3C22×D313yes—
380C2×Dic6C22×D313yes—
381C3×C4⋊C4—23no—
382C3×C4⋊C4—33no—
383C3×C4⋊C4—33no—
384C3×C4⋊C4—36no—
385C3×C4⋊C4—33no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4C22×D313yes—
388C3×C4⋊C4C22×D313yes—
389C3×C22⋊C4—33no—
390C3×C22⋊C4—33no—
391C3×C42—23no—
392C3×C42—33no—
393C3×C42—33no—
394C3×C42—33no—
395C3×C42—33no—
396C3×C42C22×D313yes—
397C3×C42C22×D313yes—
398#217—33no—
399#217—33no—
400(C2×D3)⋊C4—33no—
401(C2×D3)⋊C4—33no—
402(C2×D3)⋊C4—33no—
403(C2×D3)⋊C4—33no—
404(C2×D3)⋊C4—33no—
405(C2×D3)⋊C4—33no—
406(C2×D3)⋊C4—33no—
407(C2×D3)⋊C4—33no—
408(C2×D3)⋊C4—33no—
409(C2×D3)⋊C4—33no—
410(C2×D3)⋊C4—63no—
411(C2×D3)⋊C4—63no—
412(C2×D3)⋊C4C22×D313yes—
413(C2×D3)⋊C4C22×D313yes—
414C4⋊Dic3—33no—
415C4⋊Dic3—33no—
416C4⋊Dic3—36no—
417C4⋊Dic3—33no—
418C4⋊Dic3—31no—
419C4⋊Dic3—63no—
420C4⋊Dic3C22×D313yes—
421C4⋊Dic3C22×D313yes—
422Dic3⋊C4—31no—
423Dic3⋊C4—31no—
424Dic3⋊C4—33no—
425Dic3⋊C4—33no—
426Dic3⋊C4—36no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—31no—
430Dic3⋊C4—33no—
431Dic3⋊C4—33no—
432Dic3⋊C4—33no—
433Dic3⋊C4—61no—
434Dic3⋊C4—63no—
435Dic3⋊C4C22×D316yes—
436Dic3⋊C4C22×D311yescharacteristic
437Dic3⋊C4C22×D313yes—
438C4×Dic3—33no—
439C4×Dic3—33no—
440C4×Dic3—33no—
441C4×Dic3—33no—
442C4×Dic3—33no—
443C4×Dic3—33no—
444C4×Dic3—63no—
445C4×Dic3C22×D313yes—
446C4×Dic3C22×D313yes—
447C4×Dic3C22×D313yes—
448C4×Dic3C22×D313yes—
449C22×C32C2511yescharacteristic
450C2×C3⋊D3—23no—
451C2×C3⋊D3—23no—
452C2×C3⋊D3C23×C416yes—
453C2×C3×D3—23no—
454C2×C3×D3—23no—
455C2×C3×D3C23×C416yes—
456C2×C3×D3C23×C412yes—
457C2×C3×D3H(5,𝔽2)12yes—
458C2×C3×D32−1+412yes—
459D32—224no—
460C32×C4—23no—
461C32×C4—21no—
462C32×C4C23×C416yes—
463C3⋊Dic3—23no—
464C3⋊Dic3—21no—
465C3⋊Dic3C23×C412yes—
466C3×Dic3—23no—
467C3×Dic3—23no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3C23×C412yes—
471C3×Dic3C23×C416yes—
472C2×#41—31no—
473C2×#41—93no—
474C2×#41—93no—
475C2×#41—916no—
476C2×#41—91no—
477C22×Q8—31no—
478C22×D4—93no—
479C23×C4—93no—
480C23×C4—96no—
481C4×Q8—31no—
482C4×Q8—31no—
483C4×Q8—33no—
484C4×Q8—33no—
485C4×Q8—93no—
486C4×Q8—93no—
487C4×Q8—91no—
488C4×Q8D3211yescharacteristic, complemented
489C4×D4—33no—
490C4×D4—33no—
491C4×D4—96no—
492C4×D4—93no—
493C4×D4—93no—
494C4×D4—96no—
495C4×D4—93no—
496C4×D4—96no—
497C4×D4—96no—
498C4×D4—93no—
499C4×D4—93no—
500C4×D4—93no—
501#117—33no—
502#117—93no—
503#117—93no—
504#117—93no—
505#117—93no—
506#117—93no—
507#117—93no—
508#117—93no—
509C2×C4⋊C4—33no—
510C2×C4⋊C4—33no—
511C2×C4⋊C4—96no—
512C2×C4⋊C4—93no—
513C2×C4⋊C4—93no—
514C2×C4⋊C4—93no—
515C2×C4⋊C4—96no—
516C2×C4⋊C4—93no—
517C2×C4⋊C4—91no—
518C2×C4⋊C4—93no—
519C2×C22⋊C4—93no—
520C2×C22⋊C4—93no—
521C2×C42—33no—
522C2×C42—93no—
523C23×C3—31no—
524C23×C3—33no—
525C22×D3—33no—
526C22×D3—33no—
527C22×D3—312no—
528C22×D3—312no—
529C22×D3—63no—
530C22×D3—66no—
531C22×D3—66no—
532C22×D3—66no—
533C22×D3—66no—
534C22×D3C23×D313yes—
535C22×D3C23×D311yescharacteristic
536C3×Q8—24no—
537C3×Q8—312no—
538C3×Q8C2×C4×D314yescomplemented
539C3×Q8C2×C4×D314yescomplemented
540C3×D4—312no—
541C2×C3×C4—23no—
542C2×C3×C4—21no—
543C2×C3×C4—23no—
544C2×C3×C4—33no—
545C2×C3×C4—31no—
546C2×C3×C4—312no—
547C2×C3×C4—312no—
548C2×C3×C4—31no—
549C2×C3×C4—33no—
550C2×C3×C4—31no—
551C2×C3×C4—33no—
552C2×C3×C4—66no—
553C2×C3×C4—62no—
554C2×C3×C4—126no—
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D313yes—
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D313yes—
559C2×C3×C4C23×D313yes—
560C2×C3×C4C23×D313yes—
561#67—324no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—34no—
565C2×Dic3—312no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—33no—
569C2×Dic3—33no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—63no—
573C2×Dic3—66no—
574C2×Dic3—62no—
575C2×Dic3—126no—
576C2×Dic3C23×D311yescharacteristic
577C2×Dic3C23×D313yes—
578C2×Dic3C23×D311yescharacteristic
579C2×Dic3C23×D313yes—
580C2×Dic3C23×D313yes—
581C2×Dic3C23×D311yescharacteristic
582D12—324no—
583D12—312no—
584D12—312no—
585D12—612no—
586D12C2×C4×D3112yescomplemented
587C4×D3—22no—
588C4×D3—26no—
589C4×D3—34no—
590C4×D3—312no—
591C4×D3—312no—
592C4×D3—312no—
593C4×D3—312no—
594C4×D3—312no—
595C4×D3—46no—
596C4×D3—612no—
597C4×D3—62no—
598C4×D3—66no—
599C4×D3—126no—
600C4×D3—126no—
601C4×D3—126no—
602C4×D3—126no—
603C4×D3—126no—
604C4×D3—246no—
605C4×D3C2×C4×D3112yes—
606C4×D3C2×C4×D3112yescomplemented
607Dic6C2×C4×D3112yescomplemented
608C2×C32C24×C411yescharacteristic
609C2×C32C2×H(5,𝔽2)11yescharacteristic
610C2×C32C2×2−1+411yescharacteristic
611C3⋊D3—26no—
612C3×D3—26no—
613C3×D3#52014yescomplemented
614C24—93no—
615#41—38no—
616#41—924no—
617#41—924no—
618#41—98no—
619C2×Q8—38no—
620C2×Q8—33no—
621C2×Q8C2×D3211yescharacteristic
622C2×D4—33no—
623C2×D4—924no—
624C2×D4—96no—
625C2×D4—93no—
626C22×C4—33no—
627C22×C4—33no—
628C22×C4—31no—
629C22×C4—33no—
630C22×C4—36no—
631C22×C4—93no—
632C22×C4—924no—
633C22×C4—96no—
634C22×C4—91no—
635C22×C4—93no—
636C22×C4—91no—
637C22×C4—93no—
638C22×C4—96no—
639C22×C4—93no—
640C22×C4—96no—
641C22×C4—3612no—
642C4⋊C4—33no—
643C4⋊C4—33no—
644C4⋊C4—36no—
645C4⋊C4—33no—
646C4⋊C4—31no—
647C4⋊C4—93no—
648C4⋊C4—93no—
649C4⋊C4—96no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—93no—
653C4⋊C4—93no—
654C4⋊C4—91no—
655C4⋊C4C2×D3213yes—
656C22⋊C4—33no—
657C22⋊C4—33no—
658C22⋊C4—93no—
659C22⋊C4—93no—
660C22⋊C4—93no—
661C22⋊C4—93no—
662C22⋊C4—93no—
663C22⋊C4—93no—
664C42—33no—
665C42—33no—
666C42—33no—
667C42—33no—
668C42—93no—
669C42—93no—
670C42—93no—
671C42C2×D3213yes—
672C22×C3—21no—
673C22×C3—32no—
674C22×C3—32no—
675C22×C3—32no—
676C22×C3—36no—
677C22×C3—63no—
678C22×C3—63no—
679C22×C3C24×D311yescharacteristic
680C22×C3C24×D311yescharacteristic
681C2×D3—23no—
682C2×D3—23no—
683C2×D3—36no—
684C2×D3—36no—
685C2×D3—66no—
686C2×D3—624no—
687C2×D3—63no—
688C2×D3—63no—
689C2×D3—63no—
690C2×D3—63no—
691C2×D3—624no—
692C2×D3—123no—
693C2×D3—123no—
694C2×D3C22×C4×D316yes—
695C2×D3C22×C4×D312yes—
696C2×D3#100712yes—
697C2×D3#100912yes—
698C3×C4—21no—
699C3×C4—23no—
700C3×C4—23no—
701C3×C4—21no—
702C3×C4—26no—
703C3×C4—32no—
704C3×C4—36no—
705C3×C4—43no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—63no—
709C3×C4—63no—
710C3×C4—61no—
711C3×C4C22×C4×D316yes—
712C3×C4C22×C4×D316yes—
713Dic3—21no—
714Dic3—23no—
715Dic3—23no—
716Dic3—21no—
717Dic3—32no—
718Dic3—32no—
719Dic3—62no—
720Dic3—61no—
721Dic3—63no—
722Dic3—63no—
723Dic3—61no—
724Dic3—123no—
725Dic3—121no—
726Dic3C22×C4×D316yes—
727Dic3C22×C4×D312yes—
728C32C2×#52011yescharacteristic, complemented, Sylow
729C23—31no—
730C23—33no—
731C23—912no—
732C23—93no—
733C23—186no—
734C23—186no—
735Q8—312no—
736Q8C4×D3214yescomplemented
737D4—312no—
738D4—924no—
739D4—912no—
740C2×C4—33no—
741C2×C4—31no—
742C2×C4—312no—
743C2×C4—312no—
744C2×C4—31no—
745C2×C4—31no—
746C2×C4—33no—
747C2×C4—33no—
748C2×C4—66no—
749C2×C4—62no—
750C2×C4—912no—
751C2×C4—94no—
752C2×C4—912no—
753C2×C4—91no—
754C2×C4—912no—
755C2×C4—91no—
756C2×C4—93no—
757C2×C4—126no—
758C2×C4—186no—
759C2×C4—182no—
760C2×C4—366no—
761C2×C4—366no—
762C2×C4—366no—
763C2×C4C22×D3211yescharacteristic
764C2×C4C22×D3213yes—
765C2×C4C22×D3213yes—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—34no—
770C2×C3—66no—
771C2×C3C23×C4×D311yescharacteristic
772C2×C3C23×C4×D311yescharacteristic
773C2×C3C2×#100711yescharacteristic
774C2×C3C2×#100911yescharacteristic
775C2×C3D3×H(5,𝔽2)11yescharacteristic
776C2×C3D3×2−1+411yescharacteristic
777D3—26no—
778D3—66no—
779D3—66no—
780D3—126no—
781D3#557414yesdirect product factor
782C22—32no—
783C22—32no—
784C22—32no—
785C22—36no—
786C22—63no—
787C22—63no—
788C22—96no—
789C22—1824no—
790C22—183no—
791C22—183no—
792C22C23×D3211yescharacteristic
793C4—21no—
794C4—23no—
795C4—32no—
796C4—36no—
797C4—61no—
798C4—61no—
799C4—63no—
800C4—63no—
801C4—92no—
802C4—181no—
803C4—183no—
804C4C2×C4×D3216yes—
805C3—21no—
806C3C2×#557411yescharacteristic, complemented
807C3D3×#52011yescharacteristic, complemented
808C2—34no—
809C2—66no—
810C2—186no—
811C2C22×C4×D3211yescharacteristic
812C2D3×#100711yescharacteristic
813C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×C4×Q8C22
socle, cosocleC22×C32C25
prime radicalC2×D3×#239C2
hypercenterC4×Q8D32
hypocenterC32C2×#520
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10596045C2semidirect
3. C3×#5574C2semidirect
4. C3×C4×D3×Q8C2semidirect
5. #10595394C2semidirect
6. D3×Q8×Dic3C2semidirect
7. #10595353C2semidirect
8. D3×#893C2semidirect
9. D32×C4⋊C4C2semidirect
10. #10594361C2semidirect
11. #10594327C2semidirect
12. C4×D3×D12C2semidirect
13. D3×#872C2semidirect
14. #10593890C2semidirect
15. #10593889C2semidirect
21. D3×#239C4semidirect
27. C32×C4×Q8C22semidirect
28. Q8×C3⋊Dic3C22semidirect
29. #64102C22semidirect
30. C4⋊C4×C3⋊D3C22semidirect
31. C4×C4⋊(C3⋊D3)C22semidirect
32. #64081C22semidirect
33. C3×Q8×Dic3C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×#893C22semidirect
37. C3×D3×C4⋊C4C22semidirect
38. C3×#887C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#872C22semidirect
42. C3×C4×Dic6C22semidirect
45. #63904C22semidirect
46. C4×#626C22semidirect
47. #63900C22semidirect
48. #63898C22semidirect
49. #63894C22semidirect
50. #63894C22semidirect
51. Dic3×D12C22semidirect
53. D3×C4⋊Dic3C22semidirect
54. #63883C22semidirect
55. #63881C22semidirect
56. #63880C22semidirect
57. #63877C22semidirect
58. #63877C22semidirect
61. D3×Dic3⋊C4C22semidirect
63. #63874C22semidirect
64. #63855C22semidirect
65. #63843C22semidirect
66. Dic3×Dic6C22semidirect
67. #63836C22semidirect
68. #63836C22semidirect
85. #5574D3direct (N × H)
87. C4×D3×Q8D3semidirect
102. #3832C2×C4semidirect
106. C3×#239C2×C4semidirect
107. C3×D3×Q8C2×C4semidirect
123. D3×D12C2×C4semidirect
125. C4×D32C2×C4semidirect
126. #3799C2×C4semidirect
127. #3796C2×C4semidirect
183. C3×C4×Q8C2×D3semidirect
184. C3×C4×Q8C2×D3semidirect
196. Q8×Dic3C2×D3semidirect
197. Q8×Dic3C2×D3semidirect
219. #893C2×D3semidirect
235. D3×C4⋊C4C2×D3semidirect
237. #887C2×D3semidirect
252. C4×D12C2×D3semidirect
263. #872C2×D3semidirect
267. C4×Dic6C2×D3semidirect
274. C32×Q8C22×C4semidirect
281. C4⋊(C3⋊D3)C22×C4semidirect
283. C4×C3⋊D3C22×C4semidirect
290. C3×D12C22×C4semidirect
295. C3×C4×D3C22×C4semidirect
296. C3×Dic6C22×C4semidirect
297. #626C22×C4semidirect
299. #624C22×C4semidirect
304. D3×Dic3C22×C4semidirect
345. #239C4×D3semidirect
346. D3×Q8C4×D3semidirect
488. C4×Q8D32semidirect
538. C3×Q8C2×C4×D3semidirect
539. C3×Q8C2×C4×D3semidirect
586. D12C2×C4×D3semidirect
606. C4×D3C2×C4×D3semidirect
607. Dic6C2×C4×D3semidirect
613. C3×D3#520semidirect
728. C32C2×#520semidirect
736. Q8C4×D32semidirect
781. D3#5574direct (N × H)
806. C3C2×#5574semidirect
807. C3D3×#520semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
#105960452
C3×#55742
C3×C4×D3×Q82
#105953942
D3×Q8×Dic32
#105953532
D3×#8932
D32×C4⋊C42
#105943612
#105943272
C4×D3×D122
D3×#8722
#105938902
#105938892
D3×#5203
C2×#55743