Finite Group Databasebeta

← D3×#5569 #11903685

Subgroups — D3×#5569 #11903685

Order 1152.

2196 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596040C211yesmaximal, characteristic, complemented
2C3×C4×D3×Q8C211yesmaximal, characteristic
3C3×#5569C211yesmaximal, characteristic, complemented
4#10595422C211yesmaximal, characteristic, complemented
5D3×Q8×Dic3C211yesmaximal, characteristic
6D3×Q8×Dic3C211yesmaximal, characteristic
7#10595351C211yesmaximal, characteristic, complemented
8D3×#890C213yesmaximal
9D3×#888C213yesmaximal
10#10594322C213yesmaximal, complemented
11#10594317C213yesmaximal, complemented
12D3×#870C213yesmaximal
13C4×D3×Dic6C213yesmaximal
14#10593853C213yesmaximal, complemented
15#10593851C213yesmaximal, complemented
16D3×#557—31nomaximal
17C2×#5569—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2213yes—
20C32×C4×Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64099C2213yes—
24#64097C2213yes—
25#64079C2213yes—
26C4×#634C2213yes—
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×D3×C4⋊C4C2213yes—
31C3×#890C2213yes—
32C3×#888C2213yes—
33C3×#887C2213yes—
34C3×C42×D3C2213yes—
35C3×#870C2213yes—
36C3×C4×Dic6C2213yes—
37C3×C4×Dic6C2213yes—
38#63919C2213yes—
39#63918C2213yes—
40C4×#627C2213yes—
41C4×#627C2213yes—
42D3×C4⋊Dic3C2213yes—
43D3×C4⋊Dic3C2213yes—
44D3×C4⋊Dic3C2213yes—
45D3×Dic3⋊C4C2216yes—
46D3×Dic3⋊C4C2211yescharacteristic
47D3×Dic3⋊C4C2213yes—
48C4×D3×Dic3C2213yes—
49C4×D3×Dic3C2213yes—
50#63872C2213yes—
51#63869C2213yes—
52#63869C2213yes—
53#63869C2213yes—
54#63867C2216yes—
55#63867C2216yes—
56#63846C2216yes—
57#63845C2216yes—
58#63844C2213yes—
59#63843C2213yes—
60#63843C2213yes—
61Dic3×Dic6C2213yes—
62Dic3×Dic6C2213yes—
63Dic3×Dic6C2213yes—
64#63840C2216yes—
65#63839C2216yes—
66#63837C2213yes—
67#63837C2213yes—
68C3×#557—31no—
69C2×C3×C4×Q8—31no—
70C2×Q8×Dic3—31no—
71C2×Q8×Dic3—31no—
72D3×C4⋊Q8—33no—
73#5721—33no—
74D3×#125—33no—
75D3×#125—33no—
76#5685—33no—
77#5685—33no—
78C4×D3×Q8—31no—
79C4×D3×Q8—31no—
80C4×D3×Q8—33no—
81C4×D3×Q8D311yescharacteristic
82#5570—31no—
83#5569—31no—
84#5569—31no—
85#5569—31no—
86#5569—31no—
87#5569—31no—
88#5569—33no—
89#5569—33no—
90#5569—33no—
91#5569—33no—
92#5569—61no—
93#5569D311yescharacteristic, direct product factor
94#5567—33no—
95C2×#890—33no—
96C2×#888—33no—
97C2×#870—33no—
98C2×C4×Dic6—33no—
99C2×C32×Q8C2311yescharacteristic
100C2×#634C2313yes—
101C3×D3×Q8Q818yescomplemented
102C2×C3×C4×D3C2313yes—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2313yes—
105C2×C3×Dic6C2313yes—
106C2×C3×Dic6C2313yes—
107C2×#627C2313yes—
108C2×#627C2313yes—
109C2×D3×Dic3C2313yes—
110C2×D3×Dic3C2311yescharacteristic
111C2×D3×Dic3C2313yes—
112C2×D3×Dic3C2311yescharacteristic
113D3×Dic6—212no—
114C32×C4⋊C4C2313yes—
115C32×C42C2313yes—
116C4⋊(C3⋊Dic3)C2313yes—
117C4⋊(C3⋊Dic3)C2313yes—
118C4⋊(C3⋊Dic3)C2313yes—
119#3750C2311yescharacteristic
120#3750C2313yes—
121#3750C2316yes—
122C4×C3⋊Dic3C2313yes—
123C4×C3⋊Dic3C2313yes—
124C3×C4⋊Dic3C2313yes—
125C3×C4⋊Dic3C2313yes—
126C3×C4⋊Dic3C2313yes—
127C3×C4⋊Dic3C2313yes—
128C3×Dic3⋊C4C2316yes—
129C3×Dic3⋊C4C2316yes—
130C3×Dic3⋊C4C2311yescharacteristic
131C3×Dic3⋊C4C2313yes—
132C3×C4×Dic3C2313yes—
133C3×C4×Dic3C2313yes—
134C3×C4×Dic3C2313yes—
135C3×C4×Dic3C2313yes—
136C3×C4×Dic3C2313yes—
137#3724C2316yes—
138#3724C2311yescharacteristic
139#3724C2313yes—
140Dic3⋊Dic3C2313yes—
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2316yes—
143Dic3⋊Dic3C2316yes—
144Dic3⋊Dic3C2311yescharacteristic
145Dic3⋊Dic3C2316yes—
146Dic3⋊Dic3C2313yes—
147Dic32C2313yes—
148Dic32C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151C2×#557—91noSylow
152C22×C3×Q8—31no—
153C2×D3×Q8—33no—
154C2×D3×Q8C2×D311yescharacteristic
155C22×Dic6—33no—
156C3×C4⋊Q8—33no—
157C3×#125—33no—
158C3×#125—33no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—33no—
164C3×C4×Q8—33no—
165C3×C4×Q8—33no—
166C3×C4×Q8C2×D311yescharacteristic
167C3×C4×Q8C2×D311yescharacteristic
168C2×C3×C4⋊C4—33no—
169C2×C3×C42—33no—
170Q8×Dic3—31no—
171Q8×Dic3—31no—
172Q8×Dic3—31no—
173Q8×Dic3—31no—
174Q8×Dic3—33no—
175Q8×Dic3—33no—
176Q8×Dic3—33no—
177Q8×Dic3—33no—
178Q8×Dic3—33no—
179Q8×Dic3—61no—
180Q8×Dic3—61no—
181Q8×Dic3C2×D311yescharacteristic
182Q8×Dic3C2×D311yescharacteristic
183Q8×Dic3C2×D311yescharacteristic
184#944—36no—
185C2×C4⋊Dic3—33no—
186C2×C4⋊Dic3—33no—
187C2×C4⋊Dic3—33no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—33no—
190C2×Dic3⋊C4—36no—
191C2×C4×Dic3—33no—
192C2×C4×Dic3—33no—
193D3×C4⋊C4—36no—
194D3×C4⋊C4—33no—
195D3×C4⋊C4—33no—
196D3×C4⋊C4—33no—
197D3×C4⋊C4—33no—
198D3×C4⋊C4—31no—
199D3×C4⋊C4C2×D313yes—
200#890—33no—
201#890—33no—
202#890—33no—
203#890—36no—
204#890—33no—
205#890—36no—
206#890—33no—
207#890—33no—
208#890—33no—
209#890—63no—
210#890C2×D313yes—
211#889—36no—
212#889—36no—
213#889—36no—
214#889—36no—
215#888—36no—
216#888—33no—
217#888—33no—
218#888—33no—
219#888—33no—
220#888—36no—
221#888—36no—
222#888—33no—
223#888—63no—
224#888C2×D313yes—
225#887—33no—
226#887—33no—
227#887—33no—
228#887—33no—
229#887—33no—
230#887C2×D313yes—
231C42×D3—33no—
232C42×D3—33no—
233C42×D3C2×D313yes—
234#870—33no—
235#870—33no—
236#870—33no—
237#870—33no—
238#870—33no—
239#870—36no—
240#870—36no—
241#870—63no—
242#870C2×D313yes—
243#869—33no—
244C4×Dic6—33no—
245C4×Dic6—33no—
246C4×Dic6—33no—
247C4×Dic6—33no—
248C4×Dic6—33no—
249C4×Dic6—33no—
250C4×Dic6—33no—
251C4×Dic6—33no—
252C4×Dic6—33no—
253C4×Dic6—33no—
254C4×Dic6—33no—
255C4×Dic6—33no—
256C4×Dic6—63no—
257C4×Dic6C2×D313yes—
258C4×Dic6C2×D313yes—
259C22×C3×D3C2411yescharacteristic
260C32×Q8C2×Q814yescomplemented
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2413yes—
263C2×C32×C4C2413yes—
264C2×C3⋊Dic3C2411yescharacteristic
265C2×C3⋊Dic3C2413yes—
266C2×C3⋊Dic3C2413yes—
267C2×C3⋊Dic3C2411yescharacteristic
268#634—26no—
269C2×C3×Dic3C2411yescharacteristic
270C2×C3×Dic3C2413yes—
271C2×C3×Dic3C2413yes—
272C2×C3×Dic3C2411yescharacteristic
273C2×C3×Dic3C2413yes—
274C2×C3×Dic3C2413yes—
275C2×C3×Dic3C2411yescharacteristic
276C3×C4×D3—26no—
277C3×C4×D3—22no—
278C3×C4×D3C2×Q8112yes—
279C3×Dic6—26no—
280C3×Dic6C2×Q8112yescomplemented
281#627—26no—
282#627—26no—
283D3×Dic3—26no—
284D3×Dic3—22no—
285D3×Dic3—26no—
286D3×Dic3#4114yes—
287#557—31no—
288#557—93no—
289#557—91no—
290#557—91no—
291#557—93no—
292#557—93no—
293#557—93no—
294#557—91no—
295C2×C4⋊Q8—93no—
296C2×#125—93no—
297C2×#125—93no—
298C2×C4×Q8—31no—
299C2×C4×Q8—93no—
300C2×C4×Q8—91no—
301C2×C4×Q8—91no—
302C2×C3×Q8—21no—
303C2×C3×Q8—38no—
304C2×C3×Q8—33no—
305C2×C3×Q8—33no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C22×C3×C4—33no—
309C22×C3×C4—31no—
310C22×C3×C4—33no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—33no—
314C22×Dic3—33no—
315D3×Q8—612no—
316D3×Q8Dic618yescomplemented
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—33no—
320C2×C4×D3—33no—
321C2×C4×D3C22×D311yescharacteristic
322C2×C4×D3C22×D313yes—
323C2×C4×D3C22×D313yes—
324C2×Dic6—33no—
325C2×Dic6—33no—
326C2×Dic6—33no—
327C2×Dic6—33no—
328C2×Dic6—33no—
329C2×Dic6—33no—
330C2×Dic6—63no—
331C2×Dic6—612no—
332C2×Dic6C22×D313yes—
333C2×Dic6C22×D313yes—
334C3×C4⋊C4—23no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—33no—
337C3×C4⋊C4—33no—
338C3×C4⋊C4—33no—
339C3×C4⋊C4—33no—
340C3×C4⋊C4—36no—
341C3×C4⋊C4—33no—
342C3×C4⋊C4—36no—
343C3×C4⋊C4C22×D313yes—
344C3×C4⋊C4C22×D313yes—
345C3×C42—23no—
346C3×C42—33no—
347C3×C42—33no—
348C3×C42—33no—
349C3×C42—33no—
350C3×C42—33no—
351C3×C42C22×D313yes—
352C3×C42C22×D313yes—
353C4⋊Dic3—33no—
354C4⋊Dic3—33no—
355C4⋊Dic3—33no—
356C4⋊Dic3—33no—
357C4⋊Dic3—33no—
358C4⋊Dic3—33no—
359C4⋊Dic3—31no—
360C4⋊Dic3—33no—
361C4⋊Dic3—33no—
362C4⋊Dic3—33no—
363C4⋊Dic3—36no—
364C4⋊Dic3—36no—
365C4⋊Dic3—36no—
366C4⋊Dic3—63no—
367C4⋊Dic3—63no—
368C4⋊Dic3—63no—
369C4⋊Dic3C22×D313yes—
370C4⋊Dic3C22×D313yes—
371C4⋊Dic3C22×D313yes—
372C4⋊Dic3C22×D313yes—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—33no—
376Dic3⋊C4—33no—
377Dic3⋊C4—36no—
378Dic3⋊C4—36no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—33no—
383Dic3⋊C4—33no—
384Dic3⋊C4—33no—
385Dic3⋊C4—36no—
386Dic3⋊C4—36no—
387Dic3⋊C4—33no—
388Dic3⋊C4—33no—
389Dic3⋊C4—36no—
390Dic3⋊C4—36no—
391Dic3⋊C4—36no—
392Dic3⋊C4—61no—
393Dic3⋊C4—63no—
394Dic3⋊C4—66no—
395Dic3⋊C4C22×D311yescharacteristic
396Dic3⋊C4C22×D313yes—
397Dic3⋊C4C22×D316yes—
398Dic3⋊C4C22×D316yes—
399C4×Dic3—33no—
400C4×Dic3—33no—
401C4×Dic3—33no—
402C4×Dic3—33no—
403C4×Dic3—33no—
404C4×Dic3—33no—
405C4×Dic3—33no—
406C4×Dic3—33no—
407C4×Dic3—33no—
408C4×Dic3—33no—
409C4×Dic3—33no—
410C4×Dic3—33no—
411C4×Dic3—63no—
412C4×Dic3—63no—
413C4×Dic3C22×D313yes—
414C4×Dic3C22×D313yes—
415C4×Dic3C22×D313yes—
416C4×Dic3C22×D313yes—
417C4×Dic3C22×D313yes—
418C22×C32C2511yescharacteristic
419C2×C3×D3C22×Q812yes—
420C2×C3×D3C2×#4112yes—
421C2×C3×D32−1+412yes—
422C32×C4—23no—
423C32×C4—21no—
424C32×C4C22×Q816yes—
425C3⋊Dic3—23no—
426C3⋊Dic3—21no—
427C3⋊Dic3—23no—
428C3⋊Dic3C2×#4112yes—
429C3×Dic3—23no—
430C3×Dic3—23no—
431C3×Dic3—21no—
432C3×Dic3—23no—
433C3×Dic3—21no—
434C3×Dic3C22×Q816yes—
435C3×Dic3C2×#4112yes—
436C22×Q8—31no—
437C22×Q8—93no—
438C4⋊Q8—33no—
439C4⋊Q8—93no—
440C4⋊Q8—96no—
441C4⋊Q8—93no—
442C4⋊Q8—96no—
443C4⋊Q8—93no—
444#125—33no—
445#125—33no—
446#125—96no—
447#125—96no—
448#125—93no—
449#125—93no—
450#125—93no—
451#125—96no—
452#125—96no—
453#125—93no—
454#125—93no—
455#125—93no—
456C4×Q8—31no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—33no—
460C4×Q8—33no—
461C4×Q8—33no—
462C4×Q8—93no—
463C4×Q8—93no—
464C4×Q8—93no—
465C4×Q8—93no—
466C4×Q8—93no—
467C4×Q8—93no—
468C4×Q8—93no—
469C4×Q8—93no—
470C4×Q8—93no—
471C4×Q8—93no—
472C4×Q8—91no—
473C4×Q8—91no—
474C4×Q8—93no—
475C4×Q8D3211yescharacteristic
476C2×C4⋊C4—33no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—93no—
479C2×C4⋊C4—93no—
480C2×C4⋊C4—93no—
481C2×C4⋊C4—93no—
482C2×C4⋊C4—96no—
483C2×C42—33no—
484C2×C42—93no—
485C2×C42—93no—
486C23×C3—31no—
487C22×D3C23×D311yescharacteristic
488C3×Q8—24no—
489C3×Q8—312no—
490C3×Q8—66no—
491C3×Q8C2×Dic614yescomplemented
492C3×Q8D3×Q814yescomplemented
493C2×C3×C4—23no—
494C2×C3×C4—21no—
495C2×C3×C4—23no—
496C2×C3×C4—33no—
497C2×C3×C4—31no—
498C2×C3×C4—312no—
499C2×C3×C4—31no—
500C2×C3×C4—33no—
501C2×C3×C4—33no—
502C2×C3×C4—31no—
503C2×C3×C4—33no—
504C2×C3×C4—66no—
505C2×C3×C4—62no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D313yes—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D313yes—
510C2×C3×C4C23×D313yes—
511C2×C3×C4C23×D313yes—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—34no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—33no—
518C2×Dic3—33no—
519C2×Dic3—33no—
520C2×Dic3—33no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—63no—
524C2×Dic3—63no—
525C2×Dic3—66no—
526C2×Dic3—62no—
527C2×Dic3—66no—
528C2×Dic3C23×D311yescharacteristic
529C2×Dic3C23×D313yes—
530C2×Dic3C23×D313yes—
531C2×Dic3C23×D311yescharacteristic
532C2×Dic3C23×D313yes—
533C2×Dic3C23×D313yes—
534C2×Dic3C23×D311yescharacteristic
535C4×D3—22no—
536C4×D3—26no—
537C4×D3—34no—
538C4×D3—62no—
539C4×D3—66no—
540C4×D3—66no—
541C4×D3C2×Dic6112yes—
542Dic6—26no—
543Dic6—66no—
544Dic6—66no—
545Dic6—66no—
546Dic6—66no—
547Dic6—66no—
548Dic6—66no—
549Dic6—126no—
550Dic6C2×Dic6112yescomplemented
551C2×C32C23×Q811yescharacteristic
552C2×C32C22×#4111yescharacteristic
553C2×C32C2×2−1+411yescharacteristic
554C3×D3#55714yescomplemented
555C2×Q8—38no—
556C2×Q8—33no—
557C2×Q8—33no—
558C2×Q8—93no—
559C2×Q8—93no—
560C2×Q8—93no—
561C2×Q8—1812no—
562C2×Q8C2×D3211yescharacteristic
563C22×C4—33no—
564C22×C4—31no—
565C22×C4—33no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4—93no—
569C22×C4—93no—
570C4⋊C4—36no—
571C4⋊C4—33no—
572C4⋊C4—31no—
573C4⋊C4—33no—
574C4⋊C4—33no—
575C4⋊C4—33no—
576C4⋊C4—33no—
577C4⋊C4—36no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—93no—
581C4⋊C4—96no—
582C4⋊C4—93no—
583C4⋊C4—93no—
584C4⋊C4—93no—
585C4⋊C4—96no—
586C4⋊C4—96no—
587C4⋊C4—96no—
588C4⋊C4—91no—
589C4⋊C4—93no—
590C4⋊C4—93no—
591C4⋊C4—93no—
592C4⋊C4—93no—
593C4⋊C4—96no—
594C4⋊C4C2×D3213yes—
595C42—33no—
596C42—33no—
597C42—33no—
598C42—33no—
599C42—33no—
600C42—93no—
601C42—93no—
602C42—93no—
603C42—93no—
604C42—93no—
605C42—93no—
606C42C2×D3213yes—
607C22×C3—21no—
608C22×C3—32no—
609C22×C3—32no—
610C22×C3—32no—
611C22×C3C24×D311yescharacteristic
612C22×C3C24×D311yescharacteristic
613C2×D3C22×Dic612yes—
614C2×D3#100712yes—
615C2×D3D3×#4112yes—
616C3×C4—21no—
617C3×C4—23no—
618C3×C4—23no—
619C3×C4—21no—
620C3×C4—26no—
621C3×C4—36no—
622C3×C4—32no—
623C3×C4—43no—
624C3×C4—41no—
625C3×C4—61no—
626C3×C4—63no—
627C3×C4—63no—
628C3×C4—63no—
629C3×C4—61no—
630C3×C4C22×Dic616yes—
631C3×C4C2×D3×Q816yes—
632Dic3—21no—
633Dic3—23no—
634Dic3—23no—
635Dic3—21no—
636Dic3—23no—
637Dic3—32no—
638Dic3—32no—
639Dic3—62no—
640Dic3—61no—
641Dic3—63no—
642Dic3—63no—
643Dic3—63no—
644Dic3—61no—
645Dic3—63no—
646Dic3—123no—
647Dic3—121no—
648Dic3—123no—
649Dic3C22×Dic616yes—
650Dic3D3×#4112yes—
651C32C2×#55711yescharacteristic, complemented, Sylow
652C23—31no—
653Q8—312no—
654Q8—66no—
655Q8—186no—
656Q8—186no—
657Q8—186no—
658Q8D3×Dic614yescomplemented
659C2×C4—31no—
660C2×C4—33no—
661C2×C4—312no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—33no—
665C2×C4—33no—
666C2×C4—33no—
667C2×C4—66no—
668C2×C4—62no—
669C2×C4—94no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—93no—
673C2×C4—93no—
674C2×C4—186no—
675C2×C4—182no—
676C2×C4—186no—
677C2×C4C22×D3211yescharacteristic
678C2×C4C22×D3213yes—
679C2×C4C22×D3213yes—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—34no—
684C2×C3C23×Dic611yescharacteristic
685C2×C3C22×D3×Q811yescharacteristic
686C2×C3C2×#100711yescharacteristic
687C2×C3C2×D3×#4111yescharacteristic
688C2×C3C2×D3×#4111yescharacteristic
689C2×C3D3×2−1+411yescharacteristic
690D3#556914yesdirect product factor
691C22—32no—
692C22—32no—
693C22—32no—
694C22C23×D3211yescharacteristic
695C4—21no—
696C4—23no—
697C4—36no—
698C4—32no—
699C4—61no—
700C4—61no—
701C4—63no—
702C4—63no—
703C4—63no—
704C4—92no—
705C4—181no—
706C4—183no—
707C4—183no—
708C4C2×D3×Dic616yes—
709C3—21no—
710C3C2×#556911yescharacteristic, complemented
711C3D3×#55711yescharacteristic, complemented
712C2—34no—
713C2C22×D3×Dic611yescharacteristic
714C2D3×#100711yescharacteristic
715C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3×D3C24
hypercenterC4×Q8D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596040C2semidirect
3. C3×#5569C2semidirect
4. #10595422C2semidirect
7. #10595351C2semidirect
10. #10594322C2semidirect
11. #10594317C2semidirect
14. #10593853C2semidirect
15. #10593851C2semidirect
93. #5569D3direct (N × H)
101. C3×D3×Q8Q8semidirect
260. C32×Q8C2×Q8semidirect
280. C3×Dic6C2×Q8semidirect
316. D3×Q8Dic6semidirect
491. C3×Q8C2×Dic6semidirect
492. C3×Q8D3×Q8semidirect
550. Dic6C2×Dic6semidirect
554. C3×D3#557semidirect
651. C32C2×#557semidirect
658. Q8D3×Dic6semidirect
690. D3#5569direct (N × H)
710. C3C2×#5569semidirect
711. C3D3×#557semidirect

Maximal subgroups

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

subgroupindex
#105960402
C3×C4×D3×Q82
C3×#55692
#105954222
D3×Q8×Dic32
#105953512
D3×#8902
D3×#8882
#105943222
#105943172
D3×#8702
C4×D3×Dic62
#105938532
#105938512
D3×#5573
C2×#55693