Finite Group Databasebeta

← C2×#11722824 #13170513

Subgroups — C2×#11722824 #13170513

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89020C211yesmaximal, characteristic
2C2×#88809C211yesmaximal, characteristic, complemented
3C2×#88788C211yesmaximal, characteristic, complemented
4C2×#88785C211yesmaximal, characteristic, complemented
5C2×C3×#3711C211yesmaximal, characteristic, complemented
6C2×C3×#3710C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#11722824C218yesmaximal, direct product factor
9C2×#63817—31nomaximal
10C2×#63804—31nomaximal
11C2×#63803—31nomaximal
12C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×C4×C3⋊D3C2211yescharacteristic
14C2×C32×C4×D3C2211yescharacteristic
15C2×#6293C411yescharacteristic
16C2×#6292C411yescharacteristic
17C2×#6291C411yescharacteristic
18C2×#6290C411yescharacteristic
19#89020C414yes—
20#89020C2214yes—
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C32×C3⋊C8C2211yescharacteristic
24C2×C32×C3⋊C8C2211yescharacteristic
25#88809C2214yescomplemented
26#88788C2214yescomplemented
27#88785C2214yescomplemented
28C3×#3711C2214yescomplemented
29C3×#3710C2214yescomplemented
30C3×D3×C3⋊C8C2214yescomplemented
31C2×#3828—31no—
32C2×#3798—31no—
33C2×#3798—31no—
34C2×#3798—61no—
35C2×#3743—31no—
36C2×C8×C3⋊D3—31no—
37C2×C3×#208—31no—
38C22×C3×C3⋊C8—31no—
39C2×C3×ΓL(1,𝔽25)—31no—
40C2×C3×D3×C8—31no—
41C2×C3×D3×C8—31no—
42C2×C3×D3×C8—31no—
43C2×#3712—31no—
44C2×#3712—31no—
45C2×#3712—31no—
46C2×#3712—61no—
47C2×#3711—31no—
48C2×#3711—31no—
49C2×#3711D311yescharacteristic, complemented
50#63817—38no—
51C2×#3710—31no—
52C2×#3710—31no—
53C2×#3710—61no—
54C2×#3710D311yescharacteristic, complemented
55C2×D3×C3⋊C8D311yescharacteristic, complemented
56#63804—38no—
57#63803—38no—
58C22×C3⋊(C3⋊D3)C2×C411yescharacteristic
59C22×C3×C3⋊D3C2×C411yescharacteristic
60C22×C32×D3C2×C411yescharacteristic
61C2×C33×C4C2311yescharacteristic
62C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
63C4×C3⋊(C3⋊D3)C2×C412yes—
64C4×C3⋊(C3⋊D3)C2312yes—
65C2×C3×C3⋊Dic3C2×C411yescharacteristic
66C3×C4×C3⋊D3C2×C412yes—
67C3×C4×C3⋊D3C2312yes—
68C2×C32×Dic3C2×C411yescharacteristic
69C32×C4×D3C2×C412yes—
70C32×C4×D3C2312yes—
71#6293C2×C414yes—
72#6292C2×C414yes—
73#6291C2×C414yes—
74#6290C2×C414yes—
75C3×C3⋊(C3⋊C8)C2312yes—
76C3×C3⋊(C3⋊C8)C2312yes—
77C32×C3⋊C8C2312yes—
78C32×C3⋊C8C2312yes—
79C2×#907—91no—
80C2×#901—91no—
81C2×#901—91no—
82C22×C32×C4—31no—
83C2×#638—31no—
84C2×#638—31no—
85#3828—34no—
86#3828—34no—
87C2×C4⋊(C3⋊D3)—31no—
88C2×C4×C3⋊D3—31no—
89C2×C4×C3⋊D3—31no—
90C2×C4×C3⋊D3—31no—
91C2×C4×C3⋊D3—61no—
92C2×C4×C3⋊D3—61no—
93C2×C4×C3⋊D3—61no—
94C2×C4×C3⋊D3—121no—
95C2×C4×C3⋊D3C2×D311yescharacteristic
96C2×#634—31no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—61no—
101C2×C3×C4×D3C2×D311yescharacteristic
102C2×C3×C4×D3C2×D311yescharacteristic
103C2×#627—31no—
104C2×#627—31no—
105C2×#627—61no—
106C2×#626—31no—
107C2×#626—31no—
108C2×#626—31no—
109C2×#626—31no—
110C2×#626—61no—
111C2×#626—61no—
112C2×#625—31no—
113C2×#625—31no—
114C2×#625—61no—
115#3798—34no—
116#3798—34no—
117#3798—34no—
118#3798—34no—
119#3798—64no—
120#3798—64no—
121C2×C32×C8—31no—
122C2×C32×C8—31no—
123C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
124C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
125#3743—34no—
126C8×C3⋊D3—34no—
127C3×#208—34no—
128C2×C3×C3⋊C8—21no—
129C2×C3×C3⋊C8—21no—
130C2×C3×C3⋊C8—31no—
131C2×C3×C3⋊C8—31no—
132C2×C3×C3⋊C8—31no—
133C2×C3×C3⋊C8—31no—
134C2×C3×C3⋊C8—34no—
135C2×C3×C3⋊C8—61no—
136C2×C3×C3⋊C8—61no—
137C2×C3×C3⋊C8C2×D311yescharacteristic
138C2×C3×C3⋊C8C2×D311yescharacteristic
139C2×C3×C3⋊C8C2×D311yescharacteristic
140C2×C3×C3⋊C8C2×D311yescharacteristic
141C3×ΓL(1,𝔽25)—34no—
142C3×D3×C8—34no—
143C3×D3×C8—34no—
144C3×D3×C8—34no—
145#3712—34no—
146#3712—34no—
147#3712—34no—
148#3712—64no—
149#3711—34no—
150#3711—34no—
151#3711C2×D314yescomplemented
152#3710—34no—
153#3710—34no—
154#3710—64no—
155#3710C2×D314yescomplemented
156D3×C3⋊C8C2×D314yescomplemented
157C22×C33C22×C411yescharacteristic
158C2×C3⋊(C3⋊D3)—22no—
159C2×C3⋊(C3⋊D3)C22×C412yes—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3C22×C412yes—
162C2×C32×D3—22no—
163C2×C32×D3C22×C412yes—
164C33×C4C22×C411yescharacteristic
165C33×C4C2411yescharacteristic
166C3⋊(C3⋊Dic3)C22×C412yes—
167C3×C3⋊Dic3C22×C412yes—
168C32×Dic3C22×C412yes—
169C2×#235—91no—
170C2×#235—91no—
171C2×#235—91no—
172C2×#235—181no—
173C2×C3×M16—91no—
174C22×C3×C8—91no—
175C22×C3×C8—91no—
176C2×#208—31no—
177C2×#208—91no—
178C22×C3⋊C8—31no—
179#907—98no—
180#901—98no—
181#901—98no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)—91no—
184C2×ΓL(1,𝔽25)—91no—
185C2×ΓL(1,𝔽25)—91no—
186C2×ΓL(1,𝔽25)—91no—
187C2×ΓL(1,𝔽25)—91no—
188C2×ΓL(1,𝔽25)—181no—
189C2×D3×C8—31no—
190C2×D3×C8—31no—
191C2×D3×C8—31no—
192C2×D3×C8—91no—
193C2×D3×C8—91no—
194C2×D3×C8—91no—
195C2×D3×C8—181no—
196C23×C32—31no—
197C22×C3⋊D3—31no—
198C22×C3⋊D3—31no—
199C22×C3⋊D3—31no—
200C22×C3⋊D3—61no—
201C22×C3⋊D3—61no—
202C22×C3⋊D3—61no—
203C22×C3⋊D3—121no—
204C22×C3⋊D3C4×D311yescharacteristic
205C22×C3×D3—21no—
206C22×C3×D3—31no—
207C22×C3×D3—31no—
208C22×C3×D3—61no—
209C22×C3×D3C4×D311yescharacteristic
210C22×C3×D3C4×D311yescharacteristic
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—31no—
215C2×C32×C4—32no—
216C2×C32×C4—32no—
217C2×C32×C4—41no—
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D311yescharacteristic
220C2×C32×C4C22×D311yescharacteristic
221#638—34no—
222#638—34no—
223C2×C3⋊Dic3—31no—
224C2×C3⋊Dic3—31no—
225C2×C3⋊Dic3—31no—
226C2×C3⋊Dic3—61no—
227C2×C3⋊Dic3—61no—
228C2×C3⋊Dic3—61no—
229C2×C3⋊Dic3—121no—
230C2×C3⋊Dic3C4×D311yescharacteristic
231C4⋊(C3⋊D3)—34no—
232C4×C3⋊D3—32no—
233C4×C3⋊D3—32no—
234C4×C3⋊D3—32no—
235C4×C3⋊D3—32no—
236C4×C3⋊D3—32no—
237C4×C3⋊D3—32no—
238C4×C3⋊D3—62no—
239C4×C3⋊D3—62no—
240C4×C3⋊D3—62no—
241C4×C3⋊D3—62no—
242C4×C3⋊D3—62no—
243C4×C3⋊D3—62no—
244C4×C3⋊D3—122no—
245C4×C3⋊D3—122no—
246C4×C3⋊D3C4×D312yes—
247C4×C3⋊D3C22×D312yes—
248#634—34no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—31no—
252C2×C3×Dic3—61no—
253C2×C3×Dic3C4×D311yescharacteristic
254C2×C3×Dic3C4×D311yescharacteristic
255C3×C4×D3—22no—
256C3×C4×D3—22no—
257C3×C4×D3—32no—
258C3×C4×D3—32no—
259C3×C4×D3—32no—
260C3×C4×D3—32no—
261C3×C4×D3—62no—
262C3×C4×D3—62no—
263C3×C4×D3C4×D312yes—
264C3×C4×D3C4×D312yes—
265C3×C4×D3C22×D312yes—
266C3×C4×D3C22×D312yes—
267#627—34no—
268#627—34no—
269#627—64no—
270#626—34no—
271#626—34no—
272#626—34no—
273#626—34no—
274#626—64no—
275#626—64no—
276#625—34no—
277#625—34no—
278#625—64no—
279C32×C8—32no—
280C32×C8—32no—
281C3⋊(C3⋊C8)C22×D312yes—
282C3⋊(C3⋊C8)C22×D312yes—
283C3×C3⋊C8—22no—
284C3×C3⋊C8—22no—
285C3×C3⋊C8—32no—
286C3×C3⋊C8—32no—
287C3×C3⋊C8—32no—
288C3×C3⋊C8—32no—
289C3×C3⋊C8—62no—
290C3×C3⋊C8—62no—
291C3×C3⋊C8C22×D312yes—
292C3×C3⋊C8C22×D312yes—
293C3×C3⋊C8C22×D312yes—
294C3×C3⋊C8C22×D312yes—
295C2×#131—271noSylow
296C2×C33#13112yescomplemented
297C2×C33C23×C411yescharacteristic
298C3⋊(C3⋊D3)—22no—
299C3×C3⋊D3—22no—
300C32×D3—22no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4—91no—
305C2×#67—91no—
306C2×#67—91no—
307C2×#67—91no—
308C2×#67—91no—
309C2×#67—91no—
310C2×#67—91no—
311C2×#67—181no—
312C2×#67—181no—
313#235—94no—
314#235—94no—
315#235—94no—
316#235—94no—
317#235—94no—
318#235—94no—
319#235—184no—
320#235—184no—
321C2×D12—91no—
322C2×D12—91no—
323C2×D12—91no—
324C2×D12—181no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—91no—
329C2×C4×D3—91no—
330C2×C4×D3—91no—
331C2×C4×D3—181no—
332C2×C4×D3—181no—
333C2×C4×D3—181no—
334C2×C4×D3—361no—
335C2×C4×D3D3211yescharacteristic
336C2×Dic6—91no—
337C2×Dic6—91no—
338C2×Dic6—91no—
339C2×Dic6—181no—
340C3×M16—94no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—61no—
346C2×C3×C8—61no—
347C2×C3×C8—94no—
348C2×C3×C8—94no—
349C2×C3×C8—91no—
350C2×C3×C8—91no—
351#208—34no—
352#208—94no—
353C2×C3⋊C8—31no—
354C2×C3⋊C8—31no—
355C2×C3⋊C8—31no—
356C2×C3⋊C8—31no—
357C2×C3⋊C8—34no—
358C2×C3⋊C8—61no—
359C2×C3⋊C8—61no—
360C2×C3⋊C8D3211yescharacteristic
361C2×C3⋊C8D3211yescharacteristic
362ΓL(1,𝔽25)—34no—
363ΓL(1,𝔽25)—94no—
364ΓL(1,𝔽25)—94no—
365ΓL(1,𝔽25)—94no—
366ΓL(1,𝔽25)—94no—
367ΓL(1,𝔽25)—94no—
368ΓL(1,𝔽25)—184no—
369D3×C8—34no—
370D3×C8—34no—
371D3×C8—34no—
372D3×C8—94no—
373D3×C8—94no—
374D3×C8—94no—
375D3×C8—184no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—32no—
380C22×C32—41no—
381C22×C32—62no—
382C22×C32C2×C4×D311yescharacteristic
383C22×C32C2×C4×D311yescharacteristic
384C22×C32C2×C4×D311yescharacteristic
385C2×C3⋊D3—22no—
386C2×C3⋊D3—32no—
387C2×C3⋊D3—32no—
388C2×C3⋊D3—32no—
389C2×C3⋊D3—62no—
390C2×C3⋊D3—62no—
391C2×C3⋊D3—62no—
392C2×C3⋊D3—62no—
393C2×C3⋊D3—64no—
394C2×C3⋊D3—62no—
395C2×C3⋊D3—62no—
396C2×C3⋊D3—122no—
397C2×C3⋊D3—122no—
398C2×C3⋊D3—122no—
399C2×C3⋊D3—124no—
400C2×C3⋊D3C2×C4×D312yes—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—32no—
405C2×C3×D3—32no—
406C2×C3×D3—42no—
407C2×C3×D3—62no—
408C2×C3×D3—62no—
409C2×C3×D3—62no—
410C2×C3×D3—122no—
411C2×C3×D3C2×C4×D312yes—
412C2×C3×D3C2×C4×D312yes—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—21no—
419C32×C4—32no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×C4×D311yescharacteristic
423C32×C4C2×C4×D311yescharacteristic
424C32×C4C2×C4×D311yescharacteristic
425C32×C4C23×D311yescharacteristic
426C32×C4C23×D311yescharacteristic
427C32×C4C23×D311yescharacteristic
428C3⋊Dic3—32no—
429C3⋊Dic3—32no—
430C3⋊Dic3—32no—
431C3⋊Dic3—62no—
432C3⋊Dic3—62no—
433C3⋊Dic3—62no—
434C3⋊Dic3—122no—
435C3⋊Dic3C2×C4×D312yes—
436C3×Dic3—22no—
437C3×Dic3—32no—
438C3×Dic3—32no—
439C3×Dic3—62no—
440C3×Dic3C2×C4×D312yes—
441C3×Dic3C2×C4×D312yes—
442C2×#41—271no—
443#131—278no—
444C2×M16—91no—
445C2×M16—271no—
446C2×M16—271no—
447C22×C8—91no—
448C22×C8—91no—
449C22×C8—271no—
450C33C2×#13111yescharacteristic, complemented, Sylow
451C23×C3—31no—
452C23×C3—31no—
453C23×C3—61no—
454C23×C3—91no—
455C22×D3—31no—
456C22×D3—31no—
457C22×D3—61no—
458C22×D3—91no—
459C22×D3—91no—
460C22×D3—91no—
461C22×D3—181no—
462C22×D3—181no—
463C22×D3—181no—
464C22×D3—361no—
465C22×D3#62411yescharacteristic
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—41no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—61no—
479C2×C3×C4—91no—
480C2×C3×C4—92no—
481C2×C3×C4—92no—
482C2×C3×C4C2×D3211yescharacteristic
483C2×C3×C4C2×D3211yescharacteristic
484C2×C3×C4C2×D3211yescharacteristic
485#67—94no—
486#67—94no—
487#67—94no—
488#67—94no—
489#67—94no—
490#67—94no—
491#67—184no—
492#67—184no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—61no—
496C2×Dic3—91no—
497C2×Dic3—91no—
498C2×Dic3—91no—
499C2×Dic3—181no—
500C2×Dic3—181no—
501C2×Dic3—181no—
502C2×Dic3—361no—
503C2×Dic3#62411yescharacteristic
504D12—94no—
505D12—94no—
506D12—94no—
507D12—184no—
508C4×D3—32no—
509C4×D3—32no—
510C4×D3—32no—
511C4×D3—32no—
512C4×D3—62no—
513C4×D3—62no—
514C4×D3—92no—
515C4×D3—92no—
516C4×D3—92no—
517C4×D3—92no—
518C4×D3—92no—
519C4×D3—92no—
520C4×D3—182no—
521C4×D3—182no—
522C4×D3—182no—
523C4×D3—182no—
524C4×D3—182no—
525C4×D3—182no—
526C4×D3—362no—
527C4×D3—362no—
528C4×D3#62412yes—
529C4×D3C2×D3212yes—
530Dic6—94no—
531Dic6—94no—
532Dic6—94no—
533Dic6—184no—
534C3×C8—32no—
535C3×C8—32no—
536C3×C8—32no—
537C3×C8—32no—
538C3×C8—62no—
539C3×C8—62no—
540C3×C8—92no—
541C3×C8—92no—
542C3⋊C8—32no—
543C3⋊C8—32no—
544C3⋊C8—32no—
545C3⋊C8—32no—
546C3⋊C8—62no—
547C3⋊C8—62no—
548C3⋊C8C2×D3212yes—
549C3⋊C8C2×D3212yes—
550C2×C32—21no—
551C2×C32—21no—
552C2×C32—22no—
553C2×C32—22no—
554C2×C32—21no—
555C2×C32—22no—
556C2×C32—42no—
557C2×C32—41no—
558C2×C32—62no—
559C2×C32#90112yescomplemented
560C2×C32#90112yescomplemented
561C2×C32#90712yescomplemented
562C2×C32C22×C4×D311yescharacteristic
563C2×C32C22×C4×D311yescharacteristic
564C2×C32C22×C4×D311yescharacteristic
565C3⋊D3—22no—
566C3⋊D3—62no—
567C3⋊D3—64no—
568C3⋊D3—62no—
569C3⋊D3—62no—
570C3⋊D3—122no—
571C3⋊D3—122no—
572C3⋊D3—124no—
573C3×D3—22no—
574C3×D3—22no—
575C3×D3—42no—
576C3×D3—62no—
577C3×D3—62no—
578C3×D3—122no—
579#41—274no—
580#41—274no—
581C2×Q8—271no—
582C2×D4—271no—
583C2×D4—271no—
584C2×D4—271no—
585C22×C4—31no—
586C22×C4—91no—
587C22×C4—271no—
588M16—94no—
589M16—274no—
590M16—274no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—94no—
594C2×C8—94no—
595C2×C8—91no—
596C2×C8—91no—
597C2×C8—274no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—32no—
602C22×C3—32no—
603C22×C3—41no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—92no—
608C22×C3—122no—
609C22×C3—182no—
610C22×C3C4×D3211yescharacteristic
611C22×C3C4×D3211yescharacteristic
612C22×C3C2×#62411yescharacteristic
613C2×D3—22no—
614C2×D3—32no—
615C2×D3—32no—
616C2×D3—62no—
617C2×D3—62no—
618C2×D3—62no—
619C2×D3—92no—
620C2×D3—92no—
621C2×D3—92no—
622C2×D3—122no—
623C2×D3—182no—
624C2×D3—182no—
625C2×D3—182no—
626C2×D3—184no—
627C2×D3—182no—
628C2×D3—182no—
629C2×D3—182no—
630C2×D3—362no—
631C2×D3—362no—
632C2×D3—362no—
633C2×D3—364no—
634C2×D3C2×#62412yes—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—32no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—62no—
646C3×C4—92no—
647C3×C4C4×D3211yescharacteristic
648C3×C4C4×D3211yescharacteristic
649C3×C4C2×#62411yescharacteristic
650C3×C4C22×D3211yescharacteristic
651C3×C4C22×D3211yescharacteristic
652C3×C4C22×D3211yescharacteristic
653Dic3—32no—
654Dic3—32no—
655Dic3—62no—
656Dic3—92no—
657Dic3—92no—
658Dic3—92no—
659Dic3—182no—
660Dic3—182no—
661Dic3—182no—
662Dic3—362no—
663Dic3C2×#62412yes—
664C32—21no—
665C32—21no—
666C32—21no—
667C32—41no—
668C32C2×#90111yescharacteristic, complemented
669C32C2×#90111yescharacteristic, complemented
670C32C2×#90711yescharacteristic, complemented
671C23—31no—
672C23—91no—
673C23—271no—
674Q8—274no—
675D4—274no—
676D4—274no—
677D4—274no—
678C2×C4—31no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—91no—
682C2×C4—92no—
683C2×C4—92no—
684C2×C4—271no—
685C2×C4—272no—
686C2×C4—272no—
687C2×C4D3311yescharacteristic
688C8—32no—
689C8—32no—
690C8—92no—
691C8—92no—
692C2×C3—22no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—42no—
699C2×C3—41no—
700C2×C3—62no—
701C2×C3—62no—
702C2×C3—122no—
703C2×C3—182no—
704C2×C3#6380312yescomplemented
705C2×C3#6380412yescomplemented
706C2×C3#6381712yescomplemented
707C2×C3C2×C4×D3211yescharacteristic
708C2×C3C2×C4×D3211yescharacteristic
709C2×C3C22×#62411yescharacteristic
710D3—22no—
711D3—62no—
712D3—62no—
713D3—122no—
714D3—184no—
715D3—182no—
716D3—182no—
717D3—182no—
718D3—362no—
719D3—362no—
720D3—364no—
721C22—32no—
722C22—62no—
723C22—92no—
724C22—182no—
725C22—272no—
726C22—542no—
727C22D3×#62411yescharacteristic
728C4—32no—
729C4—92no—
730C4—272no—
731C4D3×#62411yescharacteristic
732C4C2×D3311yescharacteristic
733C3—21no—
734C3—21no—
735C3—21no—
736C3—41no—
737C3C2×#6380311yescharacteristic, complemented
738C3C2×#6380411yescharacteristic, complemented
739C3C2×#6381711yescharacteristic, complemented
740C2—62no—
741C2—182no—
742C2—542no—
743C2#1172282412yesdirect product factor
744C2C2×D3×#62411yescharacteristic
subgroupG/H
center, hypercenterC2×C4D33
commutatorC2×C33C23×C4
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C22×C4
prime radicalC2×#89020C2
cosocleC33×C4C24
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88809C2semidirect
3. C2×#88788C2semidirect
4. C2×#88785C2semidirect
5. C2×C3×#3711C2semidirect
6. C2×C3×#3710C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. #11722824C2direct (N × H)
25. #88809C22semidirect
26. #88788C22semidirect
27. #88785C22semidirect
28. C3×#3711C22semidirect
29. C3×#3710C22semidirect
30. C3×D3×C3⋊C8C22semidirect
49. C2×#3711D3semidirect
54. C2×#3710D3semidirect
55. C2×D3×C3⋊C8D3semidirect
151. #3711C2×D3semidirect
155. #3710C2×D3semidirect
156. D3×C3⋊C8C2×D3semidirect
296. C2×C33#131semidirect
450. C33C2×#131semidirect
559. C2×C32#901semidirect
560. C2×C32#901semidirect
561. C2×C32#907semidirect
668. C32C2×#901semidirect
669. C32C2×#901semidirect
670. C32C2×#907semidirect
704. C2×C3#63803semidirect
705. C2×C3#63804semidirect
706. C2×C3#63817semidirect
737. C3C2×#63803semidirect
738. C3C2×#63804semidirect
739. C3C2×#63817semidirect
743. C2#11722824direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890202
C2×#888092
C2×#887882
C2×#887852
C2×C3×#37112
C2×C3×#37102
C2×C3×D3×C3⋊C82
#117228242
C2×#638173
C2×#638043
C2×#638033