Finite Group Databasebeta

← C3×#80197 #11889479

Subgroups — C3×#80197 #11889479

Order 1152.

834 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×#5817C211yesmaximal, characteristic
2C3×#5641C211yesmaximal, characteristic, complemented
3C32×#451C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5C3×#5188C211yesmaximal, characteristic, complemented
6C3×#5187C211yesmaximal, characteristic, complemented
7C3×#5185C211yesmaximal, characteristic, complemented
8C3×#5184C211yesmaximal, characteristic, complemented
9C3×#5049C211yesmaximal, characteristic, complemented
10C3×#4815C211yesmaximal, characteristic, complemented
11C3×#4804C211yesmaximal, characteristic, complemented
12C3×#4794C211yesmaximal, characteristic, complemented
13C3×#4793C211yesmaximal, characteristic, complemented
14C3×#4737C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic, complemented
16C3×#3313—31nomaximal
17#80197C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C3×#947—21no—
24C3×#947C2211yescharacteristic
25C3×#946—21no—
26C3×#946C2211yescharacteristic
27C3×#946C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#930—21no—
32C3×#930C2211yescharacteristic
33C3×C4×#67—21no—
34C3×C4×#67C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C2×C3×#208C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#898—21no—
39C3×#892C2211yescharacteristic
40C3×#888C2211yescharacteristic
41C3×#887—21no—
42C3×#885—21no—
43C3×#879—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#835C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#818C2211yescharacteristic
56C3×#817C2211yescharacteristic
57C3×#815C2211yescharacteristic
58C3×Dic3⋊C8C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#556—31no—
62C3×#548—31no—
63#5817C2×C311yescharacteristic
64#5641C2×C311yescharacteristic, complemented
65C3×#489—31no—
66C3×#485—31no—
67C3×#482—31no—
68C3×#477—31no—
69C3×#468—31no—
70C3×#467—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#451—21no—
74C3×#451D311yescharacteristic, complemented
75C3×#451C2×C311yescharacteristic, complemented
76C3×#441—31no—
77C3×#435—31no—
78C3×#419—31no—
79C3×#416—31no—
80#5225C2×C311yescharacteristic, complemented
81#5188C2×C311yescharacteristic, complemented
82#5187C2×C311yescharacteristic, complemented
83#5185C2×C311yescharacteristic, complemented
84#5184C2×C311yescharacteristic, complemented
85#5049C2×C311yescharacteristic, complemented
86#4815C2×C311yescharacteristic, complemented
87#4804C2×C311yescharacteristic, complemented
88#4794C2×C311yescharacteristic, complemented
89#4793C2×C311yescharacteristic, complemented
90#4737C2×C311yescharacteristic, complemented
91#4728C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×Q8C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×#239—22no—
103C3×#239—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109C32×Q16—22no—
110C32×Q16—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#215—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
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⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C3×#208—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3313—31noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—21no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C22×C311yescharacteristic
149C2×#239C22×C311yescharacteristic
150C2×C3×Q16—21no—
151C2×C3×Q16—21no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C2×C3×Q16C22×C311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×SD16—31no—
157C2×C3×M16—31no—
158C22×C3×C8—31no—
159C3×C4⋊Q8—31no—
160C3×#126—61no—
161C3×#126—61no—
162C3×#124—31no—
163C3×#124—61no—
164C3×#124—61no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C22×C311yescharacteristic
171C3×#121—31no—
172C3×#121—61no—
173C3×C4×Q8—31no—
174C3×C4×Q8—31no—
175C3×C4×Q8—61no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C3×#117—31no—
180#947—21no—
181#947C22×C311yescharacteristic
182#946—21no—
183#946C22×C311yescharacteristic
184#946C22×C311yescharacteristic
185Q8×Dic3C22×C311yescharacteristic
186Q8×Dic3C22×C311yescharacteristic
187C2×#215C22×C311yescharacteristic
188#930—21no—
189#930C22×C311yescharacteristic
190C4×#67—21no—
191C4×#67C22×C311yescharacteristic
192#926C22×C311yescharacteristic
193C2×#208C22×C311yescharacteristic
194C2×D3×C8C22×C311yescharacteristic
195#898—21no—
196#892C22×C311yescharacteristic
197#888C22×C311yescharacteristic
198#887—21no—
199#885—21no—
200#879—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103C2×D311yescharacteristic
213C3×#103C2×D311yescharacteristic
214C3×#103C22×C311yescharacteristic
215C3×#103C22×C311yescharacteristic
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×#97—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232#818C22×C311yescharacteristic
233#817C22×C311yescharacteristic
234#815C22×C311yescharacteristic
235Dic3⋊C8C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—21no—
246C32×Q8—42no—
247C32×Q8#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—41no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#548—31no—
278#489—31no—
279#485—31no—
280#482—31no—
281#477—31no—
282#468—31no—
283#467—31no—
284#464—31no—
285#452—31no—
286#451C3×D311yescharacteristic, complemented
287#441—31no—
288#435—31no—
289#419—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—22no—
296C2×C3×Q8—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8—41no—
301C2×C3×Q8—42no—
302C2×C3×Q8—41no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—61no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C23×C311yescharacteristic
310C2×C3×Q8C23×C311yescharacteristic
311C2×C3×Q8C23×C311yescharacteristic
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—41no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C2×#67—21no—
325C2×#67C3×D411yescharacteristic
326#239—22no—
327#239—41no—
328C2×D12—21no—
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3C23×C311yescharacteristic
332C2×Dic6—21no—
333C3×Q16—22no—
334C3×Q16—22no—
335C3×Q16—42no—
336C3×Q16—41no—
337C3×Q16—41no—
338C3×Q16—42no—
339C3×SD16—121no—
340C3×M16—121no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—31no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42—61no—
382#217—21no—
383#217C3×D411yescharacteristic
384#215—41no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4C3×D411yescharacteristic
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C23×C311yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396C4⋊Dic3C23×C311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4C3×D411yescharacteristic
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C23×C311yescharacteristic
406#208—41no—
407C2×C3⋊C8C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409D3×C8—41no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—22no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×#41—31no—
434C22×Q8C2×C3×D311yescharacteristic
435C2×Q16C2×C3×D311yescharacteristic
436C2×Q16C2×C3×D311yescharacteristic
437C2×SD16—31no—
438C2×M16—31no—
439C22×C8—31no—
440C4⋊Q8—31no—
441#126—61no—
442#126—61no—
443#124—31no—
444#124—61no—
445#124—61no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—61no—
449C22⋊Q8C2×C3×D311yescharacteristic
450#121—31no—
451#121—61no—
452C4×Q8—31no—
453C4×Q8—31no—
454C4×Q8—61no—
455C4×D4—31no—
456C4×D4—61no—
457#117—31no—
458#117—31no—
459#107—31no—
460#107—31no—
461#106—31no—
462C4⋊C8—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103C2×C3×D311yescharacteristic
469#103C2×C3×D311yescharacteristic
470#102—31no—
471#102—31no—
472#102—31no—
473C22⋊C8—31no—
474C22⋊C8C2×C3×D311yescharacteristic
475#97—31no—
476C23×C3—21no—
477C23×C3—31no—
478C23×C3—61no—
479C23×C3D3×D411yescharacteristic
480C23×C3C2×C3×D411yescharacteristic
481C22×D3—21no—
482C22×D3C2×C3×D411yescharacteristic
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—22no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—42no—
500C3×Q8—42no—
501C3×Q8—44no—
502C3×Q8—122no—
503C3×Q8#23712yes—
504C3×Q8C3×#4112yes—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—121no—
509C3×D4—122no—
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—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—44no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4D3×D411yescharacteristic
543C2×C3×C4C2×C3×D411yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C24×C311yescharacteristic
546#67—41no—
547#67—42no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553C2×Dic3C2×C3×D411yescharacteristic
554D12—21no—
555D12—21no—
556D12—42no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—42no—
560Dic6—42no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—41no—
572C2×C32#54611yescharacteristic
573C2×C32#57511yescharacteristic
574C2×C32#57811yescharacteristic
575C3×D3—41no—
576C3×D3—81no—
577#41—62no—
578#41—121no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—41no—
582C2×Q8—61no—
583C2×Q8C22×C3×D311yescharacteristic
584C2×Q8C22×C3×D311yescharacteristic
585C2×Q8C22×C3×D311yescharacteristic
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—61no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4C22×C3×D311yescharacteristic
594Q16—22no—
595Q16—41no—
596SD16—121no—
597M16—121no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—121no—
601C2×C8C22×C3×D311yescharacteristic
602C2×C8C22×C3×D311yescharacteristic
603C4⋊C4—21no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4C22×C3×D311yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C42—31no—
625C42—61no—
626C42—61no—
627C42—61no—
628C42—61no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C22×C3×D411yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—41no—
660C3×C4—42no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C2×#23711yescharacteristic
677C3×C4#100411yescharacteristic
678C3×C4C2×C3×#4111yescharacteristic
679C3×C4C3×H(5,𝔽2)11yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686C32#331311yescharacteristic, complemented, Sylow
687C23—31no—
688C23—61no—
689C23C3×D3×D411yescharacteristic
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—21no—
695Q8—42no—
696Q8—122no—
697Q8C3×#23712yes—
698D4—61no—
699D4—61no—
700D4—122no—
701D4—121no—
702D4—122no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—42no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—122no—
719C2×C4C3×D3×D411yescharacteristic
720C2×C4C23×C3×D311yescharacteristic
721C8—21no—
722C8—21no—
723C8—61no—
724C8—61no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—42no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—121no—
732C2×C3—241no—
733C2×C3#559111yescharacteristic
734C2×C3#576611yescharacteristic
735C2×C3#577711yescharacteristic
736C2×C3C3×#54611yescharacteristic
737C2×C3C3×#57511yescharacteristic
738C2×C3C3×#57811yescharacteristic
739D3—41no—
740D3—81no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22C2×C3×D3×D411yescharacteristic
751C4—21no—
752C4—22no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4C2×C3×#23711yescharacteristic
763C4C3×#100411yescharacteristic
764C3—21no—
765C3#8019711yescharacteristic, direct product factor
766C3C3×#331311yescharacteristic, complemented
767C2—41no—
768C2—121no—
769C2—241no—
770C2C3×#559111yescharacteristic
771C2C3×#576611yescharacteristic
772C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC3×#5817C2
hypercenterC3×#451D3
hypocenterC3C3×#3313
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#451

Complements

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

NH ≅ G/Ntype
2. C3×#5641C2semidirect
3. C32×#451C2semidirect
4. C3×#5225C2semidirect
5. C3×#5188C2semidirect
6. C3×#5187C2semidirect
7. C3×#5185C2semidirect
8. C3×#5184C2semidirect
9. C3×#5049C2semidirect
10. C3×#4815C2semidirect
11. C3×#4804C2semidirect
12. C3×#4794C2semidirect
13. C3×#4793C2semidirect
14. C3×#4737C2semidirect
15. C3×#4728C2semidirect
17. #80197C3direct (N × H)
64. #5641C2×C3semidirect
74. C3×#451D3semidirect
75. C3×#451C2×C3semidirect
80. #5225C2×C3semidirect
81. #5188C2×C3semidirect
82. #5187C2×C3semidirect
83. #5185C2×C3semidirect
84. #5184C2×C3semidirect
85. #5049C2×C3semidirect
86. #4815C2×C3semidirect
87. #4804C2×C3semidirect
88. #4794C2×C3semidirect
89. #4793C2×C3semidirect
90. #4737C2×C3semidirect
91. #4728C2×C3semidirect
286. #451C3×D3semidirect
686. C32#3313semidirect
765. C3#80197direct (N × H)
766. C3C3×#3313semidirect

Maximal subgroups

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

subgroupindex
C3×#58172
C3×#56412
C32×#4512
C3×#52252
C3×#51882
C3×#51872
C3×#51852
C3×#51842
C3×#50492
C3×#48152
C3×#48042
C3×#47942
C3×#47932
C3×#47372
C3×#47282
C3×#33133
#801973