Finite Group Databasebeta

← C2×#11722841 #13170580

Subgroups — C2×#11722841 #13170580

Order 1728.

1714 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic
2C2×#89019C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88785C211yesmaximal, characteristic, complemented
5C2×C3×#3717C211yesmaximal, characteristic, complemented
6C2×C3×#3716C211yesmaximal, characteristic, complemented
7C2×C3×#3715C211yesmaximal, characteristic, complemented
8#11722841C218yesmaximal, direct product factor
9C2×#63940—31nomaximal
10C2×#63930—31nomaximal
11C2×#63796—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×#6293—21no—
19C2×#6290—21no—
20C2×#6289—21no—
21#89026—22no—
22#89026C2214yes—
23#89019—22no—
24#89019C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88785C2214yescomplemented
29C3×#3717C2214yescomplemented
30C3×#3716C2214yescomplemented
31C3×#3715C2214yescomplemented
32C2×Q8×C3⋊D3—31no—
33C2×D4×C3⋊D3—31no—
34C2×#3802—31no—
35C2×#3802—31no—
36C2×#3802—61no—
37C2×#3797—31no—
38C2×#3797—31no—
39C2×#3797—61no—
40C2×C8×C3⋊D3—31no—
41C2×C3×#215—31no—
42C2×C3×#215—31no—
43C2×C3×#214—31no—
44C2×C3×#214—31no—
45C2×C3×#204—31no—
46C2×C3×#204—31no—
47#63940—38no—
48#63930—38no—
49C2×#3717—31no—
50C2×#3717D311yescharacteristic, complemented
51C2×#3716—31no—
52C2×#3716D311yescharacteristic, complemented
53C2×#3715—31no—
54C2×#3715D311yescharacteristic, complemented
55C2×#3710—31no—
56C2×#3710—31no—
57C2×#3710—61no—
58#63796—38no—
59C22×C3⋊(C3⋊D3)D411yescharacteristic
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C2×D3×C3⋊D3—24no—
63C2×D3×C3⋊D3—44no—
64C2×C33×C4C2311yescharacteristic
65C2×C3⋊(C3⋊Dic3)D411yescharacteristic
66C4×C3⋊(C3⋊D3)D412yes—
67C4×C3⋊(C3⋊D3)C2312yes—
68C2×C3×C3⋊Dic3—21no—
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)C2312yes—
71C3×#634—21no—
72C3×#634C2312yescomplemented
73C2×C32×Dic3—21no—
74C32×D12—21no—
75C32×D12C2312yes—
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78#6293—24no—
79#6290—24no—
80#6289—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×D3×SD16—91no—
84C2×D3×SD16—91no—
85C2×D3×SD16—91no—
86C23×C3⋊D3—61no—
87C22×D32—61no—
88C22×D32—61no—
89C22×D32—62no—
90C2×C32×Q8—31no—
91C2×C32×D4—31no—
92C2×#638—61no—
93Q8×C3⋊D3—34no—
94Q8×C3⋊D3—62no—
95D4×C3⋊D3—34no—
96D4×C3⋊D3—62no—
97C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
98C2×C4×C3⋊D3—31no—
99C2×C4×C3⋊D3—31no—
100C2×C4×C3⋊D3—31no—
101C2×C4×C3⋊D3—61no—
102C2×C4×C3⋊D3—61no—
103C2×C4×C3⋊D3—61no—
104C2×C4×C3⋊D3—61no—
105C2×C4×C3⋊D3—121no—
106C2×#634—61no—
107C2×#634C2×D311yescharacteristic, complemented
108C2×C3×D12—21no—
109C2×C3×D12—31no—
110C2×C3×D12—31no—
111C2×C3×D12—61no—
112C2×C3×D12C2×D311yescharacteristic
113C2×C3×D12C2×D311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—31no—
117C2×C3×Dic6—61no—
118C2×C3×Dic6C2×D311yescharacteristic, complemented
119C2×C3×Dic6C2×D311yescharacteristic, complemented
120C2×#627—61no—
121C2×#627—61no—
122C2×#627—62no—
123C2×#625—61no—
124C2×#625—61no—
125C2×#625—62no—
126C2×#624—61no—
127C2×#624—61no—
128C2×#624—62no—
129#3802—34no—
130#3802—34no—
131#3802—62no—
132#3802—62no—
133#3802—64no—
134#3802—64no—
135#3797—34no—
136#3797—34no—
137#3797—62no—
138#3797—62no—
139#3797—64no—
140#3797—64no—
141C2×C32×C8—31no—
142C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
143C8×C3⋊D3—34no—
144C3×#215—34no—
145C3×#215—34no—
146C3×#214—34no—
147C3×#214—34no—
148C2×C3×C3⋊C8—21no—
149C2×C3×C3⋊C8—31no—
150C2×C3×C3⋊C8—31no—
151C2×C3×C3⋊C8—61no—
152C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
153C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
154C3×#204—34no—
155C3×#204—34no—
156#3717—34no—
157#3717C2×D314yescomplemented
158#3716—34no—
159#3716C2×D314yescomplemented
160#3715—34no—
161#3715C2×D314yescomplemented
162#3710—34no—
163#3710—34no—
164#3710—64no—
165C22×C33C2×D411yescharacteristic
166C2×C3⋊(C3⋊D3)SD1614yescomplemented
167C2×C3⋊(C3⋊D3)C2×D412yes—
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—42no—
170C2×C32×D3—22no—
171C2×C32×D3—42no—
172D3×C3⋊D3—48no—
173C33×C4C2×D411yescharacteristic
174C33×C4C2411yescharacteristic
175C3⋊(C3⋊Dic3)C2×D412yes—
176C3×C3⋊Dic3—22no—
177C32×Dic3—22no—
178C2×D3×Q8—91no—
179C2×D3×Q8—91no—
180C2×D3×Q8—91no—
181C2×D3×Q8—181no—
182C2×D3×D4—91no—
183C2×D3×D4—91no—
184C2×D3×D4—91no—
185C2×D3×D4—181no—
186C2×C3×SD16—91no—
187C2×C3×SD16—91no—
188C2×C3×SD16—91no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—91no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214—91no—
195D3×SD16—98no—
196D3×SD16—98no—
197D3×SD16—98no—
198C2×#204—31no—
199C2×#204—31no—
200C2×#204—91no—
201C2×D3×C8—91no—
202C2×D3×C8—91no—
203C2×D3×C8—91no—
204C2×D3×C8—181no—
205C23×C32—61no—
206C22×C3⋊D3—21no—
207C22×C3⋊D3—31no—
208C22×C3⋊D3—31no—
209C22×C3⋊D3—31no—
210C22×C3⋊D3—61no—
211C22×C3⋊D3—61no—
212C22×C3⋊D3—61no—
213C22×C3⋊D3—64no—
214C22×C3⋊D3—121no—
215C22×C3⋊D3—124no—
216C22×C3×D3—22no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—62no—
220C22×C3×D3—61no—
221C22×C3×D3—61no—
222C2×D32—64no—
223C2×D32—64no—
224C2×D32—68no—
225C2×D32—124no—
226C2×D32—124no—
227C2×D32—128no—
228C32×Q8—32no—
229C32×Q8—61no—
230C32×D4—32no—
231C32×D4—61no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—41no—
236C2×C32×C4—61no—
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240#638—64no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—31no—
243C2×C3⋊Dic3—31no—
244C2×C3⋊Dic3—31no—
245C2×C3⋊Dic3—61no—
246C2×C3⋊Dic3—61no—
247C2×C3⋊Dic3—61no—
248C2×C3⋊Dic3—121no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)C22×D312yes—
251C4×C3⋊D3—32no—
252C4×C3⋊D3—32no—
253C4×C3⋊D3—32no—
254C4×C3⋊D3—32no—
255C4×C3⋊D3—32no—
256C4×C3⋊D3—32no—
257C4×C3⋊D3—62no—
258C4×C3⋊D3—62no—
259C4×C3⋊D3—62no—
260C4×C3⋊D3—62no—
261C4×C3⋊D3—62no—
262C4×C3⋊D3—62no—
263C4×C3⋊D3—64no—
264C4×C3⋊D3—122no—
265C4×C3⋊D3—122no—
266#634—21no—
267#634—64no—
268#634C22×D312yescomplemented
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C3×D12—22no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—22no—
279C3×D12—32no—
280C3×D12—32no—
281C3×D12—62no—
282C3×D12—62no—
283C3×D12—61no—
284C3×D12—61no—
285C3×D12C22×D312yes—
286C3×D12C22×D312yes—
287C3×Dic6—22no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—22no—
291C3×Dic6—32no—
292C3×Dic6—32no—
293C3×Dic6—62no—
294C3×Dic6—62no—
295C3×Dic6—61no—
296C3×Dic6—61no—
297C3×Dic6C22×D312yescomplemented
298C3×Dic6C22×D312yescomplemented
299#627—64no—
300#627—64no—
301#627—68no—
302#625—64no—
303#625—64no—
304#625—68no—
305#624—64no—
306#624—64no—
307#624—68no—
308C32×C8—32no—
309C3⋊(C3⋊C8)C22×D312yescomplemented
310C3×C3⋊C8—22no—
311C3×C3⋊C8—32no—
312C3×C3⋊C8—32no—
313C3×C3⋊C8—62no—
314C3×C3⋊C8C22×D312yescomplemented
315C3×C3⋊C8C22×D312yescomplemented
316C22×SD16—271noSylow
317C2×C33C2×SD1612yescomplemented
318C2×C33C22×D411yescharacteristic
319C3⋊(C3⋊D3)C2×SD1614yescomplemented
320C3×C3⋊D3—42no—
321C32×D3—42no—
322C23×D3—181no—
323C23×D3—181no—
324C23×D3—181no—
325C23×D3—182no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×Q8—61no—
329C2×C3×Q8—91no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—91no—
334C2×#67—181no—
335C2×#67—181no—
336C2×#67—181no—
337C2×#67—182no—
338D3×Q8—94no—
339D3×Q8—94no—
340D3×Q8—94no—
341D3×Q8—184no—
342D3×Q8—182no—
343D3×Q8—182no—
344D3×Q8—182no—
345D3×Q8—184no—
346D3×D4—94no—
347D3×D4—94no—
348D3×D4—94no—
349D3×D4—184no—
350D3×D4—182no—
351D3×D4—182no—
352D3×D4—182no—
353D3×D4—184no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12D3211yescharacteristic
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—181no—
362C2×C4×D3—181no—
363C2×C4×D3—181no—
364C2×C4×D3—181no—
365C2×C4×D3—181no—
366C2×C4×D3—181no—
367C2×C4×D3—182no—
368C2×C4×D3—361no—
369C2×Dic6—31no—
370C2×Dic6—31no—
371C2×Dic6—61no—
372C2×Dic6—181no—
373C2×Dic6—181no—
374C2×Dic6—181no—
375C2×Dic6—182no—
376C2×Dic6D3211yescharacteristic, complemented
377C3×SD16—94no—
378C3×SD16—94no—
379C3×SD16—94no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—61no—
383C2×C3×C8—91no—
384#215—34no—
385#215—34no—
386#215—94no—
387#214—34no—
388#214—34no—
389#214—94no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8D3211yescharacteristic, complemented
394#204—34no—
395#204—34no—
396#204—94no—
397D3×C8—94no—
398D3×C8—94no—
399D3×C8—94no—
400D3×C8—184no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—41no—
405C22×C32—62no—
406C22×C32—122no—
407C22×C32D3×D411yescharacteristic
408C22×C32D3×D411yescharacteristic
409C22×C32D3×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—34no—
412C2×C3⋊D3—34no—
413C2×C3⋊D3—34no—
414C2×C3⋊D3—32no—
415C2×C3⋊D3—32no—
416C2×C3⋊D3—32no—
417C2×C3⋊D3—42no—
418C2×C3⋊D3—64no—
419C2×C3⋊D3—64no—
420C2×C3⋊D3—64no—
421C2×C3⋊D3—62no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—62no—
424C2×C3⋊D3—124no—
425C2×C3⋊D3—122no—
426C2×C3⋊D3—128no—
427C2×C3×D3—24no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—44no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—64no—
434C2×C3×D3—62no—
435C2×C3×D3—62no—
436C2×C3×D3—124no—
437C2×C3×D3—122no—
438C2×C3×D3—122no—
439D32—128no—
440D32—128no—
441D32—1216no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—41no—
449C32×C4—41no—
450C32×C4—62no—
451C32×C4D3×D411yescharacteristic
452C32×C4D3×D411yescharacteristic
453C32×C4D3×D411yescharacteristic
454C32×C4C23×D311yescharacteristic
455C32×C4C23×D311yescharacteristic
456C32×C4C23×D311yescharacteristic
457C3⋊Dic3—22no—
458C3⋊Dic3—32no—
459C3⋊Dic3—32no—
460C3⋊Dic3—32no—
461C3⋊Dic3—62no—
462C3⋊Dic3—62no—
463C3⋊Dic3—62no—
464C3⋊Dic3—122no—
465C3×Dic3—24no—
466C3×Dic3—22no—
467C3×Dic3—22no—
468C3×Dic3—64no—
469C3×Dic3—62no—
470C3×Dic3—62no—
471C22×Q8—271no—
472C22×D4—271no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—271no—
477C2×SD16—278no—
478C22×C8—271no—
479C33C22×SD1611yescharacteristic, complemented, Sylow
480C23×C3—62no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—181no—
484C22×D3—21no—
485C22×D3—62no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—91no—
489C22×D3—91no—
490C22×D3—91no—
491C22×D3—181no—
492C22×D3—181no—
493C22×D3—181no—
494C22×D3—184no—
495C22×D3—184no—
496C22×D3—184no—
497C22×D3—188no—
498C22×D3—361no—
499C22×D3—364no—
500C22×D3—364no—
501C22×D3—364no—
502C22×D3—368no—
503C3×Q8—32no—
504C3×Q8—32no—
505C3×Q8—62no—
506C3×Q8—62no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—92no—
510C3×Q8—181no—
511C3×D4—32no—
512C3×D4—32no—
513C3×D4—62no—
514C3×D4—62no—
515C3×D4—61no—
516C3×D4—61no—
517C3×D4—92no—
518C3×D4—181no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—41no—
523C2×C3×C4—62no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—181no—
527C2×C3×C4C2×D3211yescharacteristic
528C2×C3×C4C2×D3211yescharacteristic
529C2×C3×C4C2×D3211yescharacteristic
530#67—184no—
531#67—184no—
532#67—184no—
533#67—188no—
534C2×Dic3—21no—
535C2×Dic3—62no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—181no—
542C2×Dic3—181no—
543C2×Dic3—181no—
544C2×Dic3—361no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—62no—
550D12—61no—
551D12—61no—
552D12C2×D3212yes—
553C4×D3—92no—
554C4×D3—92no—
555C4×D3—92no—
556C4×D3—92no—
557C4×D3—92no—
558C4×D3—92no—
559C4×D3—182no—
560C4×D3—182no—
561C4×D3—182no—
562C4×D3—182no—
563C4×D3—182no—
564C4×D3—182no—
565C4×D3—184no—
566C4×D3—184no—
567C4×D3—184no—
568C4×D3—188no—
569C4×D3—362no—
570C4×D3—362no—
571Dic6—21no—
572Dic6—32no—
573Dic6—32no—
574Dic6—62no—
575Dic6—62no—
576Dic6—61no—
577Dic6—61no—
578Dic6—184no—
579Dic6—184no—
580Dic6—184no—
581Dic6—188no—
582Dic6C2×D3212yescomplemented
583C3×C8—32no—
584C3×C8—32no—
585C3×C8—62no—
586C3×C8—92no—
587C3⋊C8—32no—
588C3⋊C8—32no—
589C3⋊C8—62no—
590C3⋊C8C2×D3212yescomplemented
591C2×C32—21no—
592C2×C32—22no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—22no—
596C2×C32—22no—
597C2×C32—42no—
598C2×C32—41no—
599C2×C32—122no—
600C2×C32D3×SD1612yescomplemented
601C2×C32D3×SD1612yescomplemented
602C2×C32D3×SD1612yescomplemented
603C2×C32C2×D3×D411yescharacteristic
604C2×C32C2×D3×D411yescharacteristic
605C2×C32C2×D3×D411yescharacteristic
606C3⋊D3—34no—
607C3⋊D3—34no—
608C3⋊D3—34no—
609C3⋊D3—42no—
610C3⋊D3—64no—
611C3⋊D3—64no—
612C3⋊D3—64no—
613C3⋊D3—124no—
614C3×D3—44no—
615C3×D3—42no—
616C3×D3—42no—
617C3×D3—124no—
618C3×D3—122no—
619C3×D3—122no—
620C24—541no—
621C2×Q8—31no—
622C2×Q8—91no—
623C2×Q8—274no—
624C2×Q8—541no—
625C2×Q8—542no—
626C2×D4—31no—
627C2×D4—91no—
628C2×D4—274no—
629C2×D4—542no—
630C2×D4—541no—
631C22×C4—271no—
632C22×C4—541no—
633SD16—94no—
634SD16—94no—
635SD16—94no—
636SD16—274no—
637C2×C8—31no—
638C2×C8—91no—
639C2×C8—274no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—41no—
644C22×C3—64no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—124no—
648C22×C3—122no—
649C22×C3—122no—
650C22×C3—182no—
651C22×C3—362no—
652C22×C3#380211yescharacteristic
653C22×C3#381111yescharacteristic
654C22×C3#381111yescharacteristic
655C2×D3—22no—
656C2×D3—42no—
657C2×D3—64no—
658C2×D3—62no—
659C2×D3—62no—
660C2×D3—92no—
661C2×D3—94no—
662C2×D3—92no—
663C2×D3—92no—
664C2×D3—94no—
665C2×D3—94no—
666C2×D3—124no—
667C2×D3—122no—
668C2×D3—122no—
669C2×D3—182no—
670C2×D3—182no—
671C2×D3—182no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—184no—
675C2×D3—362no—
676C2×D3—364no—
677C2×D3—368no—
678C2×D3—368no—
679C2×D3—368no—
680C2×D3—3616no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—64no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—182no—
693C3×C4#380211yescharacteristic
694C3×C4#381111yescharacteristic
695C3×C4#381111yescharacteristic
696C3×C4C22×D3211yescharacteristic
697C3×C4C22×D3211yescharacteristic
698C3×C4C22×D3211yescharacteristic
699Dic3—22no—
700Dic3—64no—
701Dic3—62no—
702Dic3—62no—
703Dic3—92no—
704Dic3—92no—
705Dic3—92no—
706Dic3—182no—
707Dic3—182no—
708Dic3—182no—
709Dic3—362no—
710C32—21no—
711C32—21no—
712C32—21no—
713C32—41no—
714C32C2×D3×SD1611yescharacteristic, complemented
715C32C2×D3×SD1611yescharacteristic, complemented
716C32C2×D3×SD1611yescharacteristic, complemented
717C23—61no—
718C23—181no—
719C23—271no—
720C23—544no—
721C23—1084no—
722Q8—32no—
723Q8—61no—
724Q8—92no—
725Q8—181no—
726Q8—544no—
727D4—32no—
728D4—61no—
729D4—92no—
730D4—181no—
731D4—544no—
732C2×C4—61no—
733C2×C4—181no—
734C2×C4—271no—
735C2×C4—272no—
736C2×C4—272no—
737C2×C4—544no—
738C2×C4D3311yescharacteristic
739C8—32no—
740C8—92no—
741C2×C3—22no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—124no—
750C2×C3—122no—
751C2×C3—122no—
752C2×C3—362no—
753C2×C3#6379612yescomplemented
754C2×C3#6393012yescomplemented
755C2×C3#6394012yescomplemented
756C2×C3C2×#380211yescharacteristic
757C2×C3C2×#381111yescharacteristic
758C2×C3C2×#381111yescharacteristic
759D3—42no—
760D3—94no—
761D3—94no—
762D3—94no—
763D3—124no—
764D3—122no—
765D3—122no—
766D3—184no—
767D3—184no—
768D3—184no—
769D3—364no—
770C22—62no—
771C22—122no—
772C22—182no—
773C22—274no—
774C22—272no—
775C22—362no—
776C22—1088no—
777C22#8895411yescharacteristic
778C4—62no—
779C4—182no—
780C4—272no—
781C4#8895411yescharacteristic
782C4C2×D3311yescharacteristic
783C3—21no—
784C3—21no—
785C3—21no—
786C3—41no—
787C3C2×#6379611yescharacteristic, complemented
788C3C2×#6393011yescharacteristic, complemented
789C3C2×#6394011yescharacteristic, complemented
790C2—122no—
791C2—274no—
792C2—362no—
793C2#1172284112yesdirect product factor
794C2C2×#8895411yescharacteristic
subgroupG/H
centerC22#88954
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×#89026C2
hypercenterC2×C4D33
hypocenterC33C22×SD16
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×#89019C2semidirect
3. C2×#88811C2semidirect
4. C2×#88785C2semidirect
5. C2×C3×#3717C2semidirect
6. C2×C3×#3716C2semidirect
7. C2×C3×#3715C2semidirect
8. #11722841C2direct (N × H)
15. C2×C3×#634C22semidirect
17. C2×C32×Dic6C22semidirect
24. #89019C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88811C22semidirect
28. #88785C22semidirect
29. C3×#3717C22semidirect
30. C3×#3716C22semidirect
31. C3×#3715C22semidirect
50. C2×#3717D3semidirect
52. C2×#3716D3semidirect
54. C2×#3715D3semidirect
72. C3×#634C23semidirect
77. C32×Dic6C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
107. C2×#634C2×D3semidirect
118. C2×C3×Dic6C2×D3semidirect
119. C2×C3×Dic6C2×D3semidirect
142. C2×C3⋊(C3⋊C8)C2×D3semidirect
152. C2×C3×C3⋊C8C2×D3semidirect
153. C2×C3×C3⋊C8C2×D3semidirect
157. #3717C2×D3semidirect
159. #3716C2×D3semidirect
161. #3715C2×D3semidirect
166. C2×C3⋊(C3⋊D3)SD16semidirect
268. #634C22×D3semidirect
297. C3×Dic6C22×D3semidirect
298. C3×Dic6C22×D3semidirect
309. C3⋊(C3⋊C8)C22×D3semidirect
314. C3×C3⋊C8C22×D3semidirect
315. C3×C3⋊C8C22×D3semidirect
317. C2×C33C2×SD16semidirect
319. C3⋊(C3⋊D3)C2×SD16semidirect
376. C2×Dic6D32semidirect
393. C2×C3⋊C8D32semidirect
479. C33C22×SD16semidirect
582. Dic6C2×D32semidirect
590. C3⋊C8C2×D32semidirect
600. C2×C32D3×SD16semidirect
601. C2×C32D3×SD16semidirect
602. C2×C32D3×SD16semidirect
714. C32C2×D3×SD16semidirect
715. C32C2×D3×SD16semidirect
716. C32C2×D3×SD16semidirect
753. C2×C3#63796semidirect
754. C2×C3#63930semidirect
755. C2×C3#63940semidirect
787. C3C2×#63796semidirect
788. C3C2×#63930semidirect
789. C3C2×#63940semidirect
793. C2#11722841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890262
C2×#890192
C2×#888112
C2×#887852
C2×C3×#37172
C2×C3×#37162
C2×C3×#37152
#117228412
C2×#639403
C2×#639303
C2×#637963