Finite Group Databasebeta

← #11808801

Subgroups — #11808801

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#67C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3#10592651C211yesmaximal, characteristic, complemented
4C3×#4959C211yesmaximal, characteristic
5C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
6#10591709C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591692C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591341C211yesmaximal, characteristic, complemented
12#10591298C211yesmaximal, characteristic, complemented
13#10591293C211yesmaximal, characteristic, complemented
14#10591239C211yesmaximal, characteristic, complemented
15#10591207C211yesmaximal, characteristic, complemented
16#76893—31nomaximal
17#73481—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33Dic3×#67—24no—
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42#63837—24no—
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×D4×Dic3—31no—
56C2×C4×#67—31no—
57C2×#887—31no—
58C2×C4×Dic6—31no—
59C3×#394—31no—
60C3×C4×C22⋊C4—31no—
61#5222—31no—
62C4×#217—31no—
63#4986—31no—
64#4961—31no—
65#4959D311yescharacteristic
66#4952—31no—
67#4952—31no—
68#4952—31no—
69#4952—61no—
70#4947—31no—
71#4947—31no—
72#4947—31no—
73Dic3×C22⋊C4—31no—
74Dic3×C22⋊C4—31no—
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4D311yescharacteristic, complemented
77C4×(C2×D3)⋊C4—31no—
78C4×(C2×D3)⋊C4—31no—
79#4932—31no—
80#4675—31no—
81#4673—31no—
82#4660—31no—
83#4659—31no—
84#4658—31no—
85#4648—31no—
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C3×#67—22no—
95C2×C3×#67—22no—
96C2×C3×#67—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—22no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×#627—22no—
108C2×#627—22no—
109C2×#627—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C32×C22⋊C4—22no—
114#3757—22no—
115#3757—22no—
116#3750—22no—
117C3×#217—22no—
118C3×#217—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—22no—
123C3×C4×Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129Dic32—22no—
130Dic32—22no—
131Dic32D414yes—
132#2398—91noSylow
133C22×C3×D4—31no—
134C23×C3×C4—31no—
135C22×#67C2×D311yescharacteristic
136C23×Dic3—31no—
137C23×Dic3C2×D311yescharacteristic
138C22×C4×D3—31no—
139C22×Dic6—31no—
140C22×Dic6—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C42—31no—
150C2×C3×C42—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—31no—
156C2×#217—31no—
157C2×#217—31no—
158C2×#217—61no—
159C2×#217—61no—
160C2×#217C2×D311yescharacteristic
161C2×#217C2×D311yescharacteristic
162D4×Dic3—64no—
163C4×#67—64no—
164C2×(C2×D3)⋊C4—31no—
165C2×(C2×D3)⋊C4—31no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4C2×D311yescharacteristic
168C2×(C2×D3)⋊C4C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—61no—
176C2×Dic3⋊C4C2×D311yescharacteristic
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3—31no—
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3C2×D311yescharacteristic
184C2×C4×Dic3C2×D311yescharacteristic
185#887—64no—
186C4×Dic6—64no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—61no—
209C3⋊#95—61no—
210C3⋊#95—61no—
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32#4112yes—
221C23×C32C2411yescharacteristic
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D412yes—
247C3×#67—28no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—44no—
264C2×C3×Dic3C2×D412yes—
265C2×C3×Dic3C2×D412yes—
266C2×C3×Dic3#4112yes—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270#627—28no—
271D3×Dic3—44no—
272C2×C4×Q8—91no—
273C2×C4×D4—91no—
274#400—91no—
275#400—91no—
276#397—91no—
277#397—91no—
278#394—31no—
279#394—91no—
280#393—91no—
281#393—91no—
282C4×C22⋊C4—31no—
283C4×C22⋊C4—91no—
284C4×C22⋊C4—91no—
285C4×C22⋊C4—91no—
286#376—91no—
287C24×C3—21no—
288C24×C3—31no—
289C24×C3C22×D311yescharacteristic
290C24×C3C22×D311yescharacteristic
291C23×D3C22×D311yescharacteristic
292C2×C3×D4—62no—
293C2×C3×D4—62no—
294C2×C3×D4—62no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—62no—
305C22×C3×C4—62no—
306C22×C3×C4—62no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—22no—
312C2×#67—22no—
313C2×#67—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—62no—
330C22×Dic3—62no—
331C22×Dic3—62no—
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C22×Dic3C22×D311yescharacteristic
339C2×C4×D3—62no—
340C2×C4×D3—62no—
341C2×C4×D3—62no—
342C2×Dic6—62no—
343C2×Dic6—62no—
344C2×Dic6—62no—
345C2×Dic6—62no—
346C2×Dic6—62no—
347C2×Dic6—62no—
348C3×C4⋊C4—62no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C42—62no—
357C3×C42—62no—
358#217—22no—
359#217—22no—
360#217—62no—
361#217—62no—
362#217—62no—
363#217—62no—
364#217—62no—
365#217—62no—
366#217—62no—
367#217—122no—
368#217—122no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—62no—
372(C2×D3)⋊C4—62no—
373(C2×D3)⋊C4—62no—
374C4⋊Dic3—62no—
375C4⋊Dic3—62no—
376Dic3⋊C4—22no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—122no—
382C4×Dic3—22no—
383C4×Dic3—22no—
384C4×Dic3—34no—
385C4×Dic3—34no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C32×C4—41no—
412C32×C4—41no—
413C3⋊Dic3—22no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3#12414yes—
424C22×Q8—91no—
425C22×D4—31no—
426C23×C4—31no—
427C23×C4—91no—
428C4×Q8—184no—
429C4×D4—184no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—91no—
432C2×C4⋊C4—91no—
433C2×C4⋊C4—91no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—91no—
439C2×C22⋊C4—91no—
440C2×C22⋊C4—91no—
441C2×C22⋊C4—91no—
442C2×C22⋊C4—91no—
443C2×C22⋊C4D3211yescharacteristic
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—91no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—22no—
475C23×C3—32no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3#23512yes—
489C23×C3#23712yes—
490C23×C3C23×D311yescharacteristic
491C23×C3C23×D311yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3#23712yes—
499C3×D4—68no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—124no—
540#67—28no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—44no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—124no—
594C2×Dic3#23512yes—
595C2×Dic3#23512yes—
596C2×Dic3D3×D412yes—
597C2×Dic3D3×D412yes—
598C2×Dic3#23712yes—
599C2×Dic3#23712yes—
600C4×D3—124no—
601Dic6—68no—
602Dic6—68no—
603C2×C32—42no—
604C2×C32#52511yescharacteristic
605C2×C32#52511yescharacteristic
606C2×C32C2×#12411yescharacteristic
607C2×C32#52911yescharacteristic
608C2×C32#52911yescharacteristic
609C2×C32#52911yescharacteristic
610C2×C32#52911yescharacteristic
611C3×D3—42no—
612C24—31no—
613C24C2×D3211yescharacteristic
614C2×Q8—182no—
615C2×Q8—182no—
616C2×Q8—182no—
617C2×D4—62no—
618C2×D4—62no—
619C2×D4—62no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—62no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4—182no—
637C22×C4C2×D3211yescharacteristic
638C22×C4C2×D3211yescharacteristic
639C4⋊C4—62no—
640C4⋊C4—182no—
641C4⋊C4—182no—
642C4⋊C4—182no—
643C22⋊C4—22no—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C42—62no—
654C42—62no—
655C42—94no—
656C42—182no—
657C42—182no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—62no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3C2×#23511yescharacteristic
694C22×C3C2×#23511yescharacteristic
695C22×C3C2×#23511yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×#23711yescharacteristic
699C22×C3C2×#23711yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C3×C4—34no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—62no—
734Dic3—62no—
735Dic3—122no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—241no—
743Dic3—241no—
744Dic3—241no—
745Dic3#88514yes—
746C32#239811yescharacteristic, complemented, Sylow
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—32no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23#380412yes—
761C23C22×D3211yescharacteristic
762Q8—188no—
763D4—68no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—92no—
792C2×C4—124no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—364no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—82no—
815C2×C3—122no—
816C2×C3#547911yescharacteristic
817C2×C3C2×#88511yescharacteristic
818C2×C3#552811yescharacteristic
819C2×C3#553811yescharacteristic
820C2×C3#554711yescharacteristic
821C2×C3#554711yescharacteristic
822C2×C3#555711yescharacteristic
823C2×C3#558611yescharacteristic
824C2×C3#560011yescharacteristic
825C2×C3#560011yescharacteristic
826C2×C3#560611yescharacteristic
827C2×C3#564911yescharacteristic
828C2×C3#564911yescharacteristic
829C2×C3D3×#12411yescharacteristic
830D3—42no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22D3×#23511yescharacteristic
846C22D3×#23511yescharacteristic
847C22D32×D411yescharacteristic
848C22D3×#23711yescharacteristic
849C22D3×#23711yescharacteristic
850C22D3×#23711yescharacteristic
851C22C2×#380411yescharacteristic
852C4—34no—
853C4—41no—
854C4—41no—
855C4—62no—
856C4—62no—
857C4—62no—
858C4—121no—
859C4—121no—
860C4—121no—
861C4—182no—
862C4—361no—
863C4—361no—
864C4—361no—
865C3—21no—
866C3#7348111yescharacteristic, complemented
867C3#7689311yescharacteristic, complemented
868C2—42no—
869C2—122no—
870C2#1059408611yescharacteristic
871C2#1059409811yescharacteristic
872C2D3×#88511yescharacteristic
873C2#1059428611yescharacteristic
874C2#1059494811yescharacteristic
875C2#1059512911yescharacteristic
876C2#1059518711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63837C2semidirect
3. #10592651C2semidirect
5. C3×Dic3×C22⋊C4C2semidirect
7. Dic3×#217C2semidirect
8. #10591692C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591341C2semidirect
12. #10591298C2semidirect
13. #10591293C2semidirect
14. #10591239C2semidirect
15. #10591207C2semidirect
76. Dic3×C22⋊C4D3semidirect
746. C32#2398semidirect
866. C3#73481semidirect
867. C3#76893semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#672
C2×#638372
#105926512
C3×#49592
C3×Dic3×C22⋊C42
#105917092
Dic3×#2172
#105916922
Dic3×(C2×D3)⋊C42
#105913412
#105912982
#105912932
#105912392
#105912072
#768933
#734813