Finite Group Databasebeta

← D4×#4207⋊C2 #72259337

Subgroups — D4×#4207⋊C2 #72259337

Order 2592.

1503 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4207⋊C2C212yesmaximal, complemented
2D4×#4208C211yesmaximal, characteristic, complemented
3D4×#4207C211yesmaximal, characteristic, complemented
4D4×#4207C211yesmaximal, characteristic, complemented
5#13048790C212yesmaximal, complemented
6#13048789C212yesmaximal, complemented
7#13048789C212yesmaximal, complemented
8#13048763C211yesmaximal, characteristic, complemented
9#13048762C211yesmaximal, characteristic, complemented
10#13048762C211yesmaximal, characteristic, complemented
11C4×#4207⋊C2C211yesmaximal, characteristic, complemented
12D4×((C3⋊D3)⋊C3)⋊C2—31nomaximal
13D3×D4×D9—31nomaximal
14D3×D4×D9—31nomaximal
15C22×#4208C2212yescomplemented
16C22×#4207C2212yescomplemented
17C22×#4207C2212yescomplemented
18C2×#4207⋊C2—28no—
19C2×#4207⋊C2C2211yescharacteristic
20C2×#4207⋊C2C2212yescomplemented
21C2×#4207⋊C2C2212yescomplemented
22C2×#4207⋊C2C2212yescomplemented
23D4×#737C2211yescharacteristic, complemented
24#10619984C2212yescomplemented
25#10619983C2212yescomplemented
26#10619983C2212yescomplemented
27C4⋊#4208C2211yescharacteristic, complemented
28C4×#4208C2211yescharacteristic, complemented
29C4⋊#4207C2211yescharacteristic, complemented
30C4⋊#4207C2211yescharacteristic, complemented
31C4×#4207C2211yescharacteristic, complemented
32C4×#4207C2211yescharacteristic, complemented
33#10619909C2212yescomplemented
34#10619909C2212yescomplemented
35#10619908C2211yescharacteristic, complemented
36#10619907C2212yescomplemented
37#4207⋊C4C2211yescharacteristic, complemented
38#4207⋊C4C2211yescharacteristic, complemented
39C22×((C3⋊D3)⋊C3)⋊C2—32no—
40C22×D3×D9—32no—
41C22×D3×D9—32no—
42D4×#272D311yescharacteristic
43D4×C3⋊D9D311yescharacteristic, complemented
44D4×C3⋊D9D311yescharacteristic, complemented
45D4×AGL(1,ℤ/9)—61no—
46D4×AGL(1,ℤ/9)—61no—
47D4×(C3⋊D3)⋊C3—31no—
48D4×(C3⋊D3)⋊C3—31no—
49D3×D4×C9—31no—
50D3×D4×C9—31no—
51D3×D4×C9—61no—
52C3×D4×D9—31no—
53C3×D4×D9—31no—
54#88677—32no—
55#88676—32no—
56#88676—32no—
57#88668—32no—
58#88668—32no—
59D9×#67—32no—
60D9×#67—32no—
61D3×#611—32no—
62D3×#611—32no—
63#88655—31no—
64#88654—31no—
65#88654—31no—
66C4×((C3⋊D3)⋊C3)⋊C2—31no—
67#88646—31no—
68#88646—31no—
69D9×D12—31no—
70D9×D12—31no—
71D3×D36—31no—
72D3×D36—31no—
73C4×D3×D9—31no—
74C4×D3×D9—31no—
75C22×#737C2312yescomplemented
76C2×#4208—24no—
77C2×#4208C2311yescharacteristic
78C2×#4208C2312yescomplemented
79C2×#4207—24no—
80C2×#4207—24no—
81C2×#4207C2311yescharacteristic
82C2×#4207C2311yescharacteristic
83C2×#4207C2312yescomplemented
84C2×#4207C2312yescomplemented
85#4207⋊C2—24no—
86#4207⋊C2—24no—
87#4207⋊C2—24no—
88#4207⋊C2D414yesdirect product factor
89C4×#737C2311yescharacteristic, complemented
90#66410C2311yescharacteristic, complemented
91#66409C2311yescharacteristic, complemented
92#66409C2311yescharacteristic, complemented
93D32×D4—91no—
94D32×D4—91no—
95C2×D4×D9—91no—
96C22×#272C2×D312yes—
97C22×C3⋊D9C2×D312yescomplemented
98C22×C3⋊D9C2×D312yescomplemented
99C22×AGL(1,ℤ/9)—62no—
100C22×AGL(1,ℤ/9)—62no—
101C22×(C3⋊D3)⋊C3—32no—
102C22×(C3⋊D3)⋊C3—32no—
103C22×D3×C9—32no—
104C22×D3×C9—32no—
105C22×D3×C9—62no—
106C22×C3×D9—32no—
107C22×C3×D9—32no—
108C2×((C3⋊D3)⋊C3)⋊C2—31no—
109C2×((C3⋊D3)⋊C3)⋊C2—32no—
110C2×((C3⋊D3)⋊C3)⋊C2—32no—
111C2×((C3⋊D3)⋊C3)⋊C2—32no—
112C2×((C3⋊D3)⋊C3)⋊C2—68no—
113C2×D3×D9—31no—
114C2×D3×D9—31no—
115C2×D3×D9—32no—
116C2×D3×D9—32no—
117C2×D3×D9—32no—
118C2×D3×D9—32no—
119C2×D3×D9—32no—
120C2×D3×D9—32no—
121C2×D3×D9—68no—
122C2×D3×D9—68no—
123D4×3−1+2—21no—
124D4×3−1+2—21no—
125D4×3−1+2—41no—
126D4×H(3,𝔽3)C2×D311yescharacteristic
127C3×D4×C9—21no—
128C3×D4×C9C2×D311yescharacteristic, complemented
129C3×D4×C9C2×D311yescharacteristic, complemented
130#6235C2×D312yes—
131#6233C2×D312yescomplemented
132#6233C2×D312yescomplemented
133C4⋊#272C2×D311yescharacteristic
134C4×#272C2×D311yescharacteristic
135C4⋊(C3⋊D9)C2×D311yescharacteristic, complemented
136C4⋊(C3⋊D9)C2×D311yescharacteristic, complemented
137C4×C3⋊D9C2×D311yescharacteristic, complemented
138C4×C3⋊D9C2×D311yescharacteristic, complemented
139#611⋊C3—62no—
140#611⋊C3—62no—
141#638⋊C3—32no—
142#638⋊C3—32no—
143C9×#67—32no—
144C9×#67—32no—
145C9×#67—62no—
146C3×#611—32no—
147C3×#611—32no—
148C4⋊AGL(1,ℤ/9)—61no—
149C4⋊AGL(1,ℤ/9)—61no—
150C4×AGL(1,ℤ/9)—61no—
151C4×AGL(1,ℤ/9)—61no—
152C4⋊((C3⋊D3)⋊C3)—31no—
153C4⋊((C3⋊D3)⋊C3)—31no—
154C4×(C3⋊D3)⋊C3—31no—
155C4×(C3⋊D3)⋊C3—31no—
156C9×D12—31no—
157C9×D12—31no—
158C9×D12—61no—
159C4×D3×C9—31no—
160C4×D3×C9—31no—
161C4×D3×C9—61no—
162C3×D36—31no—
163C3×D36—31no—
164C3×C4×D9—31no—
165C3×C4×D9—31no—
166#6200—32no—
167#6200—32no—
168#6199—31no—
169#6198—32no—
170((C3⋊D3)⋊C3)⋊C4—31no—
171((C3⋊D3)⋊C3)⋊C4—31no—
172#6195—32no—
173#6195—32no—
174#6194—32no—
175#6194—32no—
176D3×Dic9—31no—
177D3×Dic9—31no—
178#6192—32no—
179#6192—32no—
180(C3⋊D9)⋊C4—31no—
181(C3⋊D9)⋊C4—31no—
182Dic3×D9—31no—
183Dic3×D9—31no—
184C2×#737—22no—
185C2×#737C2411yescharacteristic
186#4208—22no—
187#4208C2×D412yescomplemented
188#4207—22no—
189#4207—22no—
190#4207C2×D412yescomplemented
191#4207C2×D412yescomplemented
192C22×D32—92no—
193C22×D32—92no—
194D4×C3⋊D3—31no—
195D4×C3⋊D3—31no—
196C3×D3×D4—31no—
197C3×D3×D4—31no—
198C3×D3×D4—61no—
199C3×D3×D4—91no—
200C3×D3×D4—91no—
201#3811—92no—
202#3811—92no—
203D3×#67—92no—
204D3×#67—92no—
205D3×#67—92no—
206D3×#67—92no—
207#3802—91no—
208#3802—91no—
209D3×D12—91no—
210D3×D12—91no—
211D3×D12—91no—
212D3×D12—91no—
213C4×D32—91no—
214C4×D32—91no—
215C23×D9—92no—
216C2×D4×C9—91no—
217C2×#611—92no—
218D4×D9—31no—
219D4×D9—31no—
220D4×D9—61no—
221D4×D9—61no—
222D4×D9—91no—
223D4×D9—91no—
224D4×D9—92no—
225D4×D9—92no—
226C2×D36—91no—
227C2×C4×D9—91no—
228C22×3−1+2—22no—
229C22×3−1+2—22no—
230C22×3−1+2—42no—
231C22×H(3,𝔽3)C22×D312yes—
232C22×C3×C9—22no—
233C22×C3×C9C22×D312yescomplemented
234C22×C3×C9C22×D312yescomplemented
235C2×#272—24no—
236C2×#272C22×D312yes—
237C2×#272C22×D311yescharacteristic
238C2×C3⋊D9—24no—
239C2×C3⋊D9—24no—
240C2×C3⋊D9C22×D311yescharacteristic
241C2×C3⋊D9C22×D311yescharacteristic
242C2×C3⋊D9C22×D312yescomplemented
243C2×C3⋊D9C22×D312yescomplemented
244C2×AGL(1,ℤ/9)—61no—
245C2×AGL(1,ℤ/9)—61no—
246C2×AGL(1,ℤ/9)—62no—
247C2×AGL(1,ℤ/9)—62no—
248C2×AGL(1,ℤ/9)—124no—
249C2×AGL(1,ℤ/9)—124no—
250C2×(C3⋊D3)⋊C3—31no—
251C2×(C3⋊D3)⋊C3—31no—
252C2×(C3⋊D3)⋊C3—32no—
253C2×(C3⋊D3)⋊C3—32no—
254C2×(C3⋊D3)⋊C3—64no—
255C2×(C3⋊D3)⋊C3—64no—
256C2×D3×C9—31no—
257C2×D3×C9—31no—
258C2×D3×C9—32no—
259C2×D3×C9—32no—
260C2×D3×C9—64no—
261C2×D3×C9—64no—
262C2×D3×C9—61no—
263C2×D3×C9—62no—
264C2×D3×C9—124no—
265C2×C3×D9—31no—
266C2×C3×D9—31no—
267C2×C3×D9—32no—
268C2×C3×D9—32no—
269C2×C3×D9—64no—
270C2×C3×D9—64no—
271((C3⋊D3)⋊C3)⋊C2—34no—
272((C3⋊D3)⋊C3)⋊C2—64no—
273((C3⋊D3)⋊C3)⋊C2—64no—
274((C3⋊D3)⋊C3)⋊C2—64no—
275D3×D9—34no—
276D3×D9—34no—
277D3×D9—64no—
278D3×D9—64no—
279D3×D9—64no—
280D3×D9—64no—
281D3×D9—64no—
282D3×D9—64no—
283C4×3−1+2—21no—
284C4×3−1+2—21no—
285C4×3−1+2—41no—
286C4×H(3,𝔽3)C22×D311yescharacteristic
287C3×C4×C9—21no—
288C3×C4×C9C22×D311yescharacteristic, complemented
289C3×C4×C9C22×D311yescharacteristic, complemented
290#1084C22×D311yescharacteristic
291C3⋊Dic9C22×D311yescharacteristic, complemented
292C3⋊Dic9C22×D311yescharacteristic, complemented
2933−1+2⋊C4—61no—
2943−1+2⋊C4—61no—
295(C3⋊Dic3)⋊C3—31no—
296(C3⋊Dic3)⋊C3—31no—
297C9×Dic3—31no—
298C9×Dic3—31no—
299C9×Dic3—61no—
300C3×Dic9—31no—
301C3×Dic9—31no—
302C2×D3×D4—271no—
303C2×D3×D4—271no—
304C2×D3×D4—271no—
305#737C22×D411yescharacteristic, complemented, Sylow
306C22×C3⋊D3—32no—
307C22×C3⋊D3—32no—
308C22×C3×D3—32no—
309C22×C3×D3—32no—
310C22×C3×D3—62no—
311C22×C3×D3—92no—
312C22×C3×D3—92no—
313C2×D32—91no—
314C2×D32—91no—
315C2×D32—92no—
316C2×D32—92no—
317C2×D32—92no—
318C2×D32—92no—
319C2×D32—92no—
320C2×D32—92no—
321C2×D32—188no—
322C2×D32—188no—
323C32×D4—21no—
324C32×D4D3211yescharacteristic
325C32×D4D3211yescharacteristic
326#638—32no—
327#638—32no—
328C4⋊(C3⋊D3)—31no—
329C4⋊(C3⋊D3)—31no—
330C4×C3⋊D3—31no—
331C4×C3⋊D3—31no—
332C3×#67—32no—
333C3×#67—32no—
334C3×#67—62no—
335C3×#67—92no—
336C3×#67—92no—
337C3×D12—31no—
338C3×D12—31no—
339C3×D12—61no—
340C3×D12—91no—
341C3×D12—91no—
342C3×C4×D3—31no—
343C3×C4×D3—31no—
344C3×C4×D3—61no—
345C3×C4×D3—91no—
346C3×C4×D3—91no—
347#626—92no—
348#626—92no—
349#626—92no—
350#626—92no—
351#625—92no—
352#625—92no—
353#624—91no—
354#624—91no—
355D3×Dic3—91no—
356D3×Dic3—91no—
357D3×Dic3—91no—
358D3×Dic3—91no—
359C23×C9—92no—
360C22×D9—32no—
361C22×D9—32no—
362C22×D9—62no—
363C22×D9—62no—
364C22×D9—91no—
365C22×D9—92no—
366C22×D9—92no—
367C22×D9—92no—
368C22×D9—188no—
369D4×C9—21no—
370D4×C9—21no—
371D4×C9—41no—
372D4×C9—92no—
373D4×C9—91no—
374D4×C9D3211yescharacteristic
375C2×C4×C9—91no—
376#611—32no—
377#611—32no—
378#611—62no—
379#611—62no—
380#611—92no—
381#611—92no—
382C2×Dic9—91no—
383D36—31no—
384D36—31no—
385D36—61no—
386D36—61no—
387D36—92no—
388C4×D9—31no—
389C4×D9—31no—
390C4×D9—61no—
391C4×D9—61no—
392C4×D9—91no—
393C4×D9—91no—
394C2×3−1+2—21no—
395C2×3−1+2—21no—
396C2×3−1+2—41no—
397C2×3−1+2—42no—
398C2×3−1+2—42no—
399C2×3−1+2—82no—
400C2×H(3,𝔽3)—22no—
401C2×H(3,𝔽3)C23×D311yescharacteristic
402C2×C3×C9—22no—
403C2×C3×C9—22no—
404C2×C3×C9—21no—
405C2×C3×C9—42no—
406C2×C3×C9C23×D311yescharacteristic
407C2×C3×C9C23×D311yescharacteristic
408#272—22no—
409#272D3×D412yes—
410C3⋊D9—22no—
411C3⋊D9—22no—
412C3⋊D9D3×D412yescomplemented
413C3⋊D9D3×D412yescomplemented
414AGL(1,ℤ/9)—62no—
415AGL(1,ℤ/9)—62no—
416AGL(1,ℤ/9)—122no—
417AGL(1,ℤ/9)—122no—
418(C3⋊D3)⋊C3—32no—
419(C3⋊D3)⋊C3—32no—
420(C3⋊D3)⋊C3—62no—
421(C3⋊D3)⋊C3—62no—
422D3×C9—32no—
423D3×C9—32no—
424D3×C9—62no—
425D3×C9—62no—
426D3×C9—62no—
427D3×C9—122no—
428C3×D9—32no—
429C3×D9—32no—
430C3×D9—62no—
431C3×D9—62no—
432C23×D3—272no—
433C23×D3—272no—
434C23×D3—272no—
435C2×C3×D4—91no—
436C2×C3×D4—271no—
437C2×C3×D4—271no—
438C2×#67—272no—
439C2×#67—272no—
440C2×#67—272no—
441D3×D4—31no—
442D3×D4—31no—
443D3×D4—61no—
444D3×D4—91no—
445D3×D4—91no—
446D3×D4—271no—
447D3×D4—271no—
448D3×D4—271no—
449D3×D4—271no—
450D3×D4—271no—
451D3×D4—271no—
452D3×D4—272no—
453D3×D4—272no—
454D3×D4—272no—
455D3×D4—272no—
456D3×D4—272no—
457D3×D4—272no—
458D3×D4—271no—
459D3×D4—541no—
460C2×D12—271no—
461C2×D12—271no—
462C2×D12—271no—
463C2×C4×D3—271no—
464C2×C4×D3—271no—
465C2×C4×D3—271no—
466C22×C32—22no—
467C22×C32C2×D3212yes—
468C22×C32C2×D3212yes—
469C2×C3⋊D3—31no—
470C2×C3⋊D3—32no—
471C2×C3⋊D3—31no—
472C2×C3⋊D3—32no—
473C2×C3⋊D3—64no—
474C2×C3⋊D3—64no—
475C2×C3×D3—31no—
476C2×C3×D3—31no—
477C2×C3×D3—32no—
478C2×C3×D3—32no—
479C2×C3×D3—61no—
480C2×C3×D3—62no—
481C2×C3×D3—64no—
482C2×C3×D3—64no—
483C2×C3×D3—91no—
484C2×C3×D3—91no—
485C2×C3×D3—92no—
486C2×C3×D3—92no—
487C2×C3×D3—124no—
488C2×C3×D3—184no—
489C2×C3×D3—184no—
490D32—94no—
491D32—94no—
492D32—184no—
493D32—184no—
494D32—184no—
495D32—184no—
496D32—184no—
497D32—184no—
498C32×C4—21no—
499C32×C4C2×D3211yescharacteristic
500C32×C4C2×D3211yescharacteristic
501C3⋊Dic3—31no—
502C3⋊Dic3—31no—
503C3×Dic3—31no—
504C3×Dic3—31no—
505C3×Dic3—61no—
506C3×Dic3—91no—
507C3×Dic3—91no—
508C22×C9—22no—
509C22×C9—22no—
510C22×C9—42no—
511C22×C9—91no—
512C22×C9—92no—
513C22×C9—184no—
514C22×C9C2×D3212yes—
515C2×D9—31no—
516C2×D9—31no—
517C2×D9—32no—
518C2×D9—32no—
519C2×D9—61no—
520C2×D9—61no—
521C2×D9—62no—
522C2×D9—62no—
523C2×D9—64no—
524C2×D9—64no—
525C2×D9—94no—
526C2×D9—124no—
527C2×D9—124no—
528C2×D9—184no—
529C2×D9—184no—
530C2×D9—184no—
531C4×C9—21no—
532C4×C9—21no—
533C4×C9—41no—
534C4×C9—91no—
535C4×C9C2×D3211yescharacteristic
536Dic9—31no—
537Dic9—31no—
538Dic9—61no—
539Dic9—61no—
540C22×D4—811noSylow
5413−1+2—21no—
5423−1+2—21no—
5433−1+2—41no—
544H(3,𝔽3)C2×D3×D411yescharacteristic
545C3×C9—21no—
546C3×C9C2×D3×D411yescharacteristic, complemented
547C3×C9C2×D3×D411yescharacteristic, complemented
548C23×C3—92no—
549C23×C3—272no—
550C23×C3—272no—
551C22×D3—32no—
552C22×D3—32no—
553C22×D3—62no—
554C22×D3—92no—
555C22×D3—92no—
556C22×D3—272no—
557C22×D3—271no—
558C22×D3—271no—
559C22×D3—272no—
560C22×D3—272no—
561C22×D3—272no—
562C22×D3—272no—
563C22×D3—272no—
564C22×D3—272no—
565C22×D3—271no—
566C22×D3—272no—
567C22×D3—272no—
568C22×D3—272no—
569C22×D3—542no—
570C22×D3—548no—
571C22×D3—548no—
572C22×D3—548no—
573C3×D4—31no—
574C3×D4—61no—
575C3×D4—92no—
576C3×D4—91no—
577C3×D4—121no—
578C3×D4—271no—
579C3×D4—271no—
580C3×D4—272no—
581C3×D4—272no—
582C3×D4#111311yescharacteristic
583C2×C3×C4—91no—
584C2×C3×C4—271no—
585C2×C3×C4—271no—
586#67—32no—
587#67—32no—
588#67—62no—
589#67—92no—
590#67—92no—
591#67—272no—
592#67—272no—
593#67—272no—
594#67—272no—
595#67—272no—
596#67—272no—
597#67—272no—
598#67—542no—
599C2×Dic3—271no—
600C2×Dic3—271no—
601C2×Dic3—271no—
602D12—31no—
603D12—31no—
604D12—61no—
605D12—91no—
606D12—91no—
607D12—271no—
608D12—272no—
609D12—272no—
610D12—272no—
611D12—541no—
612C4×D3—31no—
613C4×D3—31no—
614C4×D3—61no—
615C4×D3—91no—
616C4×D3—91no—
617C4×D3—271no—
618C4×D3—271no—
619C4×D3—271no—
620C4×D3—271no—
621C4×D3—271no—
622C4×D3—271no—
623C4×D3—271no—
624C4×D3—541no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—21no—
628C2×C32—42no—
629C2×C32C22×D3211yescharacteristic
630C2×C32C22×D3211yescharacteristic
631C3⋊D3—32no—
632C3⋊D3—32no—
633C3⋊D3—62no—
634C3⋊D3—62no—
635C3×D3—32no—
636C3×D3—32no—
637C3×D3—62no—
638C3×D3—62no—
639C3×D3—62no—
640C3×D3—92no—
641C3×D3—92no—
642C3×D3—122no—
643C3×D3—182no—
644C3×D3—182no—
645C2×C9—22no—
646C2×C9—21no—
647C2×C9—21no—
648C2×C9—42no—
649C2×C9—42no—
650C2×C9—41no—
651C2×C9—82no—
652C2×C9—92no—
653C2×C9—182no—
654C2×C9C22×D3211yescharacteristic
655D9—32no—
656D9—32no—
657D9—62no—
658D9—62no—
659D9—62no—
660D9—62no—
661D9—122no—
662D9—122no—
663C24—812no—
664C2×D4—91no—
665C2×D4—271no—
666C2×D4—271no—
667C2×D4—811no—
668C2×D4—811no—
669C2×D4—811no—
670C2×D4—812no—
671C2×D4—812no—
672C2×D4—812no—
673C22×C4—811no—
674C22×C3—32no—
675C22×C3—62no—
676C22×C3—91no—
677C22×C3—92no—
678C22×C3—122no—
679C22×C3—184no—
680C22×C3—271no—
681C22×C3—272no—
682C22×C3—271no—
683C22×C3—272no—
684C22×C3—544no—
685C22×C3—544no—
686C22×C3C2×#111312yes—
687C2×D3—31no—
688C2×D3—31no—
689C2×D3—32no—
690C2×D3—32no—
691C2×D3—61no—
692C2×D3—62no—
693C2×D3—64no—
694C2×D3—64no—
695C2×D3—91no—
696C2×D3—91no—
697C2×D3—92no—
698C2×D3—92no—
699C2×D3—124no—
700C2×D3—184no—
701C2×D3—184no—
702C2×D3—271no—
703C2×D3—272no—
704C2×D3—274no—
705C2×D3—274no—
706C2×D3—274no—
707C2×D3—541no—
708C2×D3—542no—
709C2×D3—544no—
710C2×D3—544no—
711C2×D3—544no—
712C2×D3—544no—
713C2×D3—544no—
714C2×D3—544no—
715C2×D3—544no—
716C2×D3—544no—
717C2×D3—544no—
718C2×D3—544no—
719C2×D3—1084no—
720C3×C4—31no—
721C3×C4—61no—
722C3×C4—91no—
723C3×C4—121no—
724C3×C4—271no—
725C3×C4—271no—
726C3×C4C2×#111311yescharacteristic
727Dic3—31no—
728Dic3—31no—
729Dic3—61no—
730Dic3—91no—
731Dic3—91no—
732Dic3—271no—
733Dic3—541no—
734C32—21no—
735C32D32×D411yescharacteristic
736C32D32×D411yescharacteristic
737C9—21no—
738C9—21no—
739C9—41no—
740C9D32×D411yescharacteristic
741C23—92no—
742C23—272no—
743C23—272no—
744C23—811no—
745C23—812no—
746C23—812no—
747C23—812no—
748C23—1628no—
749D4—92no—
750D4—91no—
751D4—272no—
752D4—272no—
753D4—271no—
754D4—271no—
755D4—812no—
756D4—812no—
757D4—812no—
758D4#4207⋊C211yescharacteristic, direct product factor
759C2×C4—91no—
760C2×C4—271no—
761C2×C4—271no—
762C2×C4—811no—
763C2×C4—811no—
764C2×C4—811no—
765C2×C3—22no—
766C2×C3—31no—
767C2×C3—62no—
768C2×C3—61no—
769C2×C3—92no—
770C2×C3—122no—
771C2×C3—121no—
772C2×C3—182no—
773C2×C3—242no—
774C2×C3—272no—
775C2×C3—272no—
776C2×C3—542no—
777C2×C3—542no—
778C2×C3C22×#111311yescharacteristic
779D3—32no—
780D3—32no—
781D3—62no—
782D3—62no—
783D3—62no—
784D3—92no—
785D3—92no—
786D3—122no—
787D3—182no—
788D3—182no—
789D3—272no—
790D3—542no—
791D3—542no—
792D3—1082no—
793C22—91no—
794C22—92no—
795C22—184no—
796C22—271no—
797C22—271no—
798C22—272no—
799C22—272no—
800C22—544no—
801C22—544no—
802C22—814no—
803C22—1624no—
804C22—1624no—
805C22—1624no—
806C22C2×#4207⋊C212yescomplemented
807C4—91no—
808C4—271no—
809C4—271no—
810C4C2×#4207⋊C211yescharacteristic, complemented
811C3—31no—
812C3—61no—
813C3—121no—
814C3D4×#111311yescharacteristic
815C2—22no—
816C2—92no—
817C2—182no—
818C2—272no—
819C2—272no—
820C2—542no—
821C2—542no—
822C2C22×#4207⋊C211yescharacteristic
subgroupG/H
centerC2C22×#4207⋊C2
commutator, cosocleC2×#737C24
Frattini, socleC2×C3C22×#1113
FittingD4×#737C22
hypercenterD4#4207⋊C2
hypocenter#737C22×D4
LCSG ▷ C2×#737 ▷ #737
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C22×#4207⋊C2C2semidirect
2. D4×#4208C2semidirect
3. D4×#4207C2semidirect
4. D4×#4207C2semidirect
5. #13048790C2semidirect
6. #13048789C2semidirect
7. #13048789C2semidirect
8. #13048763C2semidirect
9. #13048762C2semidirect
10. #13048762C2semidirect
11. C4×#4207⋊C2C2semidirect
15. C22×#4208C22semidirect
16. C22×#4207C22semidirect
17. C22×#4207C22semidirect
20. C2×#4207⋊C2C22semidirect
21. C2×#4207⋊C2C22semidirect
22. C2×#4207⋊C2C22semidirect
23. D4×#737C22semidirect
24. #10619984C22semidirect
25. #10619983C22semidirect
26. #10619983C22semidirect
27. C4⋊#4208C22semidirect
28. C4×#4208C22semidirect
29. C4⋊#4207C22semidirect
30. C4⋊#4207C22semidirect
31. C4×#4207C22semidirect
32. C4×#4207C22semidirect
33. #10619909C22semidirect
34. #10619909C22semidirect
35. #10619908C22semidirect
36. #10619907C22semidirect
37. #4207⋊C4C22semidirect
38. #4207⋊C4C22semidirect
43. D4×C3⋊D9D3semidirect
44. D4×C3⋊D9D3semidirect
75. C22×#737C23semidirect
78. C2×#4208C23semidirect
83. C2×#4207C23semidirect
84. C2×#4207C23semidirect
88. #4207⋊C2D4direct (N × H)
89. C4×#737C23semidirect
90. #66410C23semidirect
91. #66409C23semidirect
92. #66409C23semidirect
97. C22×C3⋊D9C2×D3semidirect
98. C22×C3⋊D9C2×D3semidirect
128. C3×D4×C9C2×D3semidirect
129. C3×D4×C9C2×D3semidirect
131. #6233C2×D3semidirect
132. #6233C2×D3semidirect
135. C4⋊(C3⋊D9)C2×D3semidirect
136. C4⋊(C3⋊D9)C2×D3semidirect
137. C4×C3⋊D9C2×D3semidirect
138. C4×C3⋊D9C2×D3semidirect
187. #4208C2×D4semidirect
190. #4207C2×D4semidirect
191. #4207C2×D4semidirect
233. C22×C3×C9C22×D3semidirect
234. C22×C3×C9C22×D3semidirect
242. C2×C3⋊D9C22×D3semidirect
243. C2×C3⋊D9C22×D3semidirect
288. C3×C4×C9C22×D3semidirect
289. C3×C4×C9C22×D3semidirect
291. C3⋊Dic9C22×D3semidirect
292. C3⋊Dic9C22×D3semidirect
305. #737C22×D4semidirect
412. C3⋊D9D3×D4semidirect
413. C3⋊D9D3×D4semidirect
546. C3×C9C2×D3×D4semidirect
547. C3×C9C2×D3×D4semidirect
758. D4#4207⋊C2direct (N × H)
806. C22C2×#4207⋊C2semidirect
810. C4C2×#4207⋊C2semidirect

Maximal subgroups

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

subgroupindex
C22×#4207⋊C22
D4×#42082
D4×#42072
#130487902
#130487892
#130487632
#130487622
C4×#4207⋊C22
D4×((C3⋊D3)⋊C3)⋊C23
D3×D4×D93