Finite Group Databasebeta

← C3×#78849 #11888006

Subgroups — C3×#78849 #11888006

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic
2C3×#5533C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5C3×#5116C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic, complemented
7C3×#4996C211yesmaximal, characteristic, complemented
8C3×#4814C211yesmaximal, characteristic, complemented
9C3×#4813C211yesmaximal, characteristic, complemented
10C3×#4795C211yesmaximal, characteristic, complemented
11C3×#4792C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4772C211yesmaximal, characteristic, complemented
14C3×#4759C211yesmaximal, characteristic, complemented
15C3×#4758C211yesmaximal, characteristic, complemented
16C3×#3302—31nomaximal
17#78849C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#929—21no—
30C3×C4×#67C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×Dic3⋊C4—21no—
34C2×C3×Dic12C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36C3×#897C2211yescharacteristic
37C3×#892C2211yescharacteristic
38C3×#888C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#885—21no—
41C3×#879—21no—
42C3×#876—21no—
43C3×C4×Dic6—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#556—31no—
62C3×#547—31no—
63#5824C2×C311yescharacteristic
64#5533C2×C311yescharacteristic, complemented
65C3×#487—31no—
66C3×#485—31no—
67C3×#485—31no—
68C3×#474—31no—
69C3×#467—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#452—31no—
73C3×#452—31no—
74C3×C4×SD16—31no—
75C3×C8×D4—31no—
76C3×#416—21no—
77C3×#416—31no—
78C3×#416D311yescharacteristic, complemented
79C3×#416C2×C311yescharacteristic, complemented
80#5239C2×C311yescharacteristic, complemented
81#5116C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic, complemented
83#4996C2×C311yescharacteristic, complemented
84#4814C2×C311yescharacteristic, complemented
85#4813C2×C311yescharacteristic, complemented
86#4795C2×C311yescharacteristic, complemented
87#4792C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic, complemented
89#4772C2×C311yescharacteristic, complemented
90#4759C2×C311yescharacteristic, complemented
91#4758C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×#214—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3302—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41—31no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C22×C311yescharacteristic
149C2×#237C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—21no—
154C22×C3×C8—31no—
155C22×C3×C8C2×D311yescharacteristic
156C22×C3×C8C22×C311yescharacteristic
157C3×C4⋊Q8—31no—
158C3×C4⋊Q8—31no—
159C3×#126—61no—
160C3×#126—61no—
161C3×#124—61no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×#121—61no—
169C3×C4×Q8—31no—
170C3×C4×Q8—61no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×#117—21no—
174C3×#117—31no—
175C3×#117C2×D311yescharacteristic
176C3×#117C22×C311yescharacteristic
177C2×C3×C4⋊C4—61no—
178#946C22×C311yescharacteristic
179#944C22×C311yescharacteristic
180C2×#216C22×C311yescharacteristic
181#939—21no—
182#935—21no—
183D4×Dic3C22×C311yescharacteristic
184C2×#214C22×C311yescharacteristic
185#929—21no—
186C4×#67C22×C311yescharacteristic
187#924C22×C311yescharacteristic
188#924C22×C311yescharacteristic
189C2×Dic3⋊C4—21no—
190C2×Dic12C22×C311yescharacteristic
191C2×D3×C8C22×C311yescharacteristic
192#897C22×C311yescharacteristic
193#892C22×C311yescharacteristic
194#888C22×C311yescharacteristic
195#887C22×C311yescharacteristic
196#885—21no—
197#879—21no—
198#876—21no—
199C4×Dic6—21no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic
212C3×#103C2×D311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#102—21no—
216C3×#102—21no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic
219C3×#102C2×D311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#835C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#818C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232Dic3⋊C8C22×C311yescharacteristic
233C8×Dic3C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4—42no—
245C32×D4#4112yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—42no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—22no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#547—31no—
278#487—31no—
279#485—31no—
280#485—31no—
281#474—31no—
282#467—31no—
283#467—31no—
284#462—31no—
285#452—31no—
286#452—31no—
287C4×SD16—31no—
288C8×D4—31no—
289#416—31no—
290#416C3×D311yescharacteristic, complemented
291C3×#41—24no—
292C3×#41—22no—
293C3×#41—22no—
294C3×#41—41no—
295C3×#41—41no—
296C3×#41—42no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—61no—
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×Q8C23×C311yescharacteristic
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—31no—
309C2×C3×D4—41no—
310C2×C3×D4—61no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C23×C311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—41no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67—21no—
323C2×#67C3×D411yescharacteristic
324C22×Dic3—21no—
325C22×Dic3—21no—
326#237—22no—
327#237—41no—
328C2×C4×D3C23×C311yescharacteristic
329C2×Dic6—21no—
330C2×Dic6C23×C311yescharacteristic
331C2×Dic6C23×C311yescharacteristic
332C3×Q16—121no—
333C3×Q16—121no—
334C3×SD16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—41no—
340C2×C3×C8—41no—
341C2×C3×C8—42no—
342C2×C3×C8—121no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—31no—
378C3×C42—41no—
379C3×C42—61no—
380C3×C42—61no—
381#217—21no—
382#217—21no—
383#217—21no—
384#217C3×D411yescharacteristic
385#216—41no—
386#214—22no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4C3×D411yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3C23×C311yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4C3×D411yescharacteristic
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407Dic12—41no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—22no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4H(5,𝔽2)11yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3#13512yes—
432C2×#41—31no—
433C2×#41C2×C3×D311yescharacteristic
434C2×Q16—31no—
435C2×Q16—31no—
436C2×SD16—31no—
437C22×C8—31no—
438C22×C8C2×C3×D311yescharacteristic
439C4⋊Q8—31no—
440C4⋊Q8—31no—
441#126—61no—
442#126—61no—
443#124—61no—
444#123—61no—
445#123—61no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450#121—61no—
451C4×Q8—31no—
452C4×Q8—61no—
453C4×D4—31no—
454C4×D4—31no—
455#117—31no—
456#117C2×C3×D311yescharacteristic
457C2×C4⋊C4—61no—
458#107—31no—
459#107—31no—
460#106—31no—
461C4⋊C8—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103C2×C3×D311yescharacteristic
468#103C2×C3×D311yescharacteristic
469#102—31no—
470#102C2×C3×D311yescharacteristic
471#102C2×C3×D311yescharacteristic
472C22⋊C8—31no—
473C22⋊C8—31no—
474C4×C8—31no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3D3×D411yescharacteristic
481C23×C3C2×C3×D411yescharacteristic
482C22×D3C2×C3×D411yescharacteristic
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—22no—
497C3×D4—41no—
498C3×D4—42no—
499C3×D4—42no—
500C3×D4—44no—
501C3×D4—62no—
502C3×D4—122no—
503C3×D4#23512yes—
504C3×D4C3×#4112yes—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—44no—
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—122no—
535C2×C3×C4—122no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4C2×C3×D411yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C24×C311yescharacteristic
540#67—22no—
541#67—42no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—42no—
547C2×Dic3—42no—
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551C4×D3—21no—
552C4×D3—21no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557Dic6—42no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—41no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C2×C32—41no—
569C2×C32—42no—
570C2×C32#54611yescharacteristic
571C2×C32C2×#13511yescharacteristic
572C2×C32#57811yescharacteristic
573C3×D3—41no—
574#41—22no—
575#41—41no—
576#41—62no—
577#41—121no—
578C2×Q8—31no—
579C2×Q8—31no—
580C2×Q8—61no—
581C2×Q8C22×C3×D311yescharacteristic
582C2×D4—21no—
583C2×D4—31no—
584C2×D4—61no—
585C2×D4C22×C3×D311yescharacteristic
586C22×C4—21no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4C22×C3×D311yescharacteristic
591Q16—121no—
592Q16—121no—
593SD16—62no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—41no—
597C2×C8—121no—
598C2×C8C22×C3×D311yescharacteristic
599C2×C8C22×C3×D311yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4C22×C3×D311yescharacteristic
612C4⋊C4C22×C3×D311yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C42—21no—
623C42—31no—
624C42—61no—
625C42—61no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×C3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23511yescharacteristic
675C3×C4#100411yescharacteristic
676C3×C4C2×C3×#4111yescharacteristic
677C3×C4C3×H(5,𝔽2)11yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3C3×#13512yes—
685C32#330211yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23C3×D3×D411yescharacteristic
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693Q8—61no—
694Q8—61no—
695Q8—122no—
696D4—21no—
697D4—42no—
698D4—62no—
699D4—122no—
700D4C3×#23512yes—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—42no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4C3×D3×D411yescharacteristic
719C2×C4C23×C3×D311yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—41no—
729C2×C3—42no—
730C2×C3—41no—
731C2×C3—42no—
732C2×C3—82no—
733C2×C3—121no—
734C2×C3#549011yescharacteristic
735C2×C3D3×#13511yescharacteristic
736C2×C3#577111yescharacteristic
737C2×C3C3×#54611yescharacteristic
738C2×C3C2×C3×#13511yescharacteristic
739C2×C3C3×#57811yescharacteristic
740D3—41no—
741C22—21no—
742C22—22no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22C2×C3×D3×D411yescharacteristic
751C4—21no—
752C4—32no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4C2×C3×#23511yescharacteristic
763C4C3×#100411yescharacteristic
764C3—21no—
765C3#7884911yescharacteristic, direct product factor
766C3C3×#330211yescharacteristic, complemented
767C2—41no—
768C2—42no—
769C2—121no—
770C2C3×#549011yescharacteristic
771C2C3×D3×#13511yescharacteristic
772C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC3×#5824C2
hypercenterC3×#416D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
2. C3×#5533C2semidirect
3. C32×#416C2semidirect
4. C3×#5239C2semidirect
5. C3×#5116C2semidirect
6. C3×C8×#67C2semidirect
7. C3×#4996C2semidirect
8. C3×#4814C2semidirect
9. C3×#4813C2semidirect
10. C3×#4795C2semidirect
11. C3×#4792C2semidirect
12. C3×#4783C2semidirect
13. C3×#4772C2semidirect
14. C3×#4759C2semidirect
15. C3×#4758C2semidirect
17. #78849C3direct (N × H)
64. #5533C2×C3semidirect
78. C3×#416D3semidirect
79. C3×#416C2×C3semidirect
80. #5239C2×C3semidirect
81. #5116C2×C3semidirect
82. C8×#67C2×C3semidirect
83. #4996C2×C3semidirect
84. #4814C2×C3semidirect
85. #4813C2×C3semidirect
86. #4795C2×C3semidirect
87. #4792C2×C3semidirect
88. #4783C2×C3semidirect
89. #4772C2×C3semidirect
90. #4759C2×C3semidirect
91. #4758C2×C3semidirect
290. #416C3×D3semidirect
685. C32#3302semidirect
765. C3#78849direct (N × H)
766. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
C3×#55332
C32×#4162
C3×#52392
C3×#51162
C3×C8×#672
C3×#49962
C3×#48142
C3×#48132
C3×#47952
C3×#47922
C3×#47832
C3×#47722
C3×#47592
C3×#47582
C3×#33023
#788493