Finite Group Databasebeta

← C3×#80103 #11887843

Subgroups — C3×#80103 #11887843

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5831C211yesmaximal, characteristic, complemented
2C3×#5614C211yesmaximal, characteristic, complemented
3C32×#449C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5C3×#5170C211yesmaximal, characteristic, complemented
6C3×Dic3×SD16C211yesmaximal, characteristic, complemented
7C3×#5157C211yesmaximal, characteristic, complemented
8C3×#5153C211yesmaximal, characteristic, complemented
9C3×#5041C211yesmaximal, characteristic, complemented
10C3×D3×#103C211yesmaximal, characteristic, complemented
11C3×#4796C211yesmaximal, characteristic, complemented
12C3×#4777C211yesmaximal, characteristic, complemented
13C3×#4768C211yesmaximal, characteristic, complemented
14C3×#67⋊C8C211yesmaximal, characteristic, complemented
15C3×#4723C211yesmaximal, characteristic, complemented
16C3×#3301—31nomaximal
17#80103C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#938—21no—
25C3×#938—21no—
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C3×#936—21no—
29C3×#936C2211yescharacteristic
30C3×#935—21no—
31C3×D4×Dic3C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×C4×#67—21no—
34C3×C4×#67C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C3×#924—21no—
37C3×#924C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic
40C3×D3×C4⋊C4C2211yescharacteristic
41C3×#890C2211yescharacteristic
42C3×#67⋊C4—21no—
43C3×#879—21no—
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#818C2211yescharacteristic
54C3×#817C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×Dic3⋊C8C2211yescharacteristic
58C3×C8×Dic3C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#553—31no—
62C3×#548—31no—
63#5831C2×C311yescharacteristic, complemented
64#5614C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#485—31no—
67C3×#481—31no—
68C3×#479—31no—
69C3×#466—31no—
70C3×#465—31no—
71C3×#463—31no—
72C3×#449—21no—
73C3×#449D311yescharacteristic, complemented
74C3×#449C2×C311yescharacteristic, complemented
75C3×#448—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#103—31no—
80#5233C2×C311yescharacteristic, complemented
81#5170C2×C311yescharacteristic, complemented
82Dic3×SD16C2×C311yescharacteristic, complemented
83#5157C2×C311yescharacteristic, complemented
84#5153C2×C311yescharacteristic, complemented
85#5041C2×C311yescharacteristic, complemented
86D3×#103C2×C311yescharacteristic, complemented
87#4796C2×C311yescharacteristic, complemented
88#4777C2×C311yescharacteristic, complemented
89#4768C2×C311yescharacteristic, complemented
90#67⋊C8C2×C311yescharacteristic, complemented
91#4723C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4—21no—
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×D3×Q8—22no—
106C3×D3×Q8—41no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C32×SD16—22no—
113C32×D8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#217D411yescharacteristic
126C3×#214—41no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
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⋊C8—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3301—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×Q8—31no—
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×SD16—21no—
151C2×C3×SD16—31no—
152C2×C3×SD16C2×D311yescharacteristic
153C2×C3×SD16C22×C311yescharacteristic
154C2×C3×D8—21no—
155C2×C3×D8C2×D311yescharacteristic
156C2×C3×D8C22×C311yescharacteristic
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#124—31no—
162C3×#124—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—61no—
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—31no—
169C3×#121—61no—
170C3×#121—61no—
171C3×#121C2×D311yescharacteristic
172C3×#121C22×C311yescharacteristic
173C3×C4×Q8—31no—
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C2×C3×C4⋊C4—31no—
180Q8×Dic3C22×C311yescharacteristic
181#938—21no—
182#938—21no—
183#938C22×C311yescharacteristic
184#938C22×C311yescharacteristic
185#936—21no—
186#936C22×C311yescharacteristic
187#935—21no—
188D4×Dic3C22×C311yescharacteristic
189C2×#214C22×C311yescharacteristic
190C4×#67—21no—
191C4×#67C22×C311yescharacteristic
192#926C22×C311yescharacteristic
193#924—21no—
194#924C22×C311yescharacteristic
195C22×C3⋊C8C22×C311yescharacteristic
196C2×D3×C8C22×C311yescharacteristic
197D3×C4⋊C4C22×C311yescharacteristic
198#890C22×C311yescharacteristic
199#67⋊C4—21no—
200#879—21no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#102—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic
225#835C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#832C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#818C22×C311yescharacteristic
231#817C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234Dic3⋊C8C22×C311yescharacteristic
235C8×Dic3C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32—21no—
240C23×C32C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8#4112yes—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—42no—
249C32×D4—81no—
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—22no—
258C3×#67—42no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—42no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—31no—
280#548—31no—
281#488—31no—
282#485—31no—
283#481—31no—
284#479—31no—
285#466—31no—
286#465—31no—
287#463—31no—
288#449C3×D311yescharacteristic, complemented
289#448—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#103—31no—
294C3×#41—22no—
295C3×#41—22no—
296C3×#41—42no—
297C3×#41—41no—
298C3×#41—41no—
299C3×#41—42no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8—61no—
303C2×C3×Q8—62no—
304C2×C3×Q8—121no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C23×C311yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—41no—
315C2×C3×D4—41no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4C22×D311yescharacteristic
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C23×C311yescharacteristic
321C2×C3×D4C23×C311yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—41no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C23×C311yescharacteristic
332C2×#67—21no—
333C2×#67—21no—
334C2×#67C3×D411yescharacteristic
335C22×Dic3—21no—
336D3×Q8—22no—
337D3×Q8—41no—
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3C23×C311yescharacteristic
341C2×Dic6—21no—
342C2×Dic6C23×C311yescharacteristic
343C3×SD16—22no—
344C3×SD16—22no—
345C3×SD16—42no—
346C3×SD16—121no—
347C3×D8—41no—
348C3×D8—41no—
349C3×D8—42no—
350C2×C3×C8—21no—
351C2×C3×C8—21no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C2×C3×C8—121no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C23×C311yescharacteristic
359C2×C3×C8C23×C311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385C3×C42—61no—
386C3×C42—61no—
387#217—21no—
388#217—21no—
389#217—21no—
390#217—21no—
391#217—21no—
392#217—21no—
393#217—21no—
394#217C3×D411yescharacteristic
395#214—41no—
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3C23×C311yescharacteristic
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4C3×D411yescharacteristic
406C4×Dic3—21no—
407C4×Dic3—21no—
408C4×Dic3C23×C311yescharacteristic
409C2×C3⋊C8—41no—
410C2×C3⋊C8C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3#13512yes—
426C32×C4—22no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41C2×C3×D311yescharacteristic
439C22×Q8—31no—
440C2×SD16—31no—
441C2×SD16C2×C3×D311yescharacteristic
442C2×D8C2×C3×D311yescharacteristic
443C22×C8—31no—
444C22×C8—31no—
445#126—61no—
446#125—31no—
447#124—31no—
448#124—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—61no—
452#121—31no—
453#121—31no—
454#121—61no—
455#121—61no—
456#121C2×C3×D311yescharacteristic
457C4×Q8—31no—
458C4×D4—31no—
459C4×D4—31no—
460C4×D4—61no—
461C4×D4—61no—
462#117—31no—
463C2×C4⋊C4—31no—
464#107—31no—
465#106—31no—
466#106—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—31no—
473#103C2×C3×D311yescharacteristic
474#102—31no—
475#102—31no—
476#102—31no—
477#102C2×C3×D311yescharacteristic
478C22⋊C8—31no—
479C22⋊C8C2×C3×D311yescharacteristic
480C4×C8—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×C3×D411yescharacteristic
491C22×D3C2×C3×D411yescharacteristic
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—22no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—122no—
499C3×Q8#23712yes—
500C3×Q8C3×#4112yes—
501C3×D4—22no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—42no—
514C3×D4—42no—
515C3×D4—44no—
516C3×D4—62no—
517C3×D4—81no—
518C3×D4—81no—
519C3×D4—82no—
520C3×D4—122no—
521C3×D4—122no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—31no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—44no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4—241no—
550C2×C3×C4—241no—
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C24×C311yescharacteristic
555#67—22no—
556#67—42no—
557#67—42no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—81no—
563C2×Dic3C2×C3×D411yescharacteristic
564C2×Dic3C2×C3×D411yescharacteristic
565C2×Dic3C2×C3×D411yescharacteristic
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—42no—
569C4×D3—81no—
570Dic6—21no—
571Dic6—21no—
572Dic6—42no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—61no—
580C3×C8—61no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—41no—
584C2×C32—81no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3×D3—22no—
590#41—22no—
591#41—41no—
592C2×Q8—31no—
593C2×Q8—61no—
594C2×Q8—62no—
595C2×Q8—121no—
596C2×Q8C22×C3×D311yescharacteristic
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—31no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4C22×C3×D311yescharacteristic
603C2×D4C22×C3×D311yescharacteristic
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4C22×C3×D311yescharacteristic
610SD16—22no—
611SD16—121no—
612D8—41no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—121no—
616C2×C8—121no—
617C2×C8C22×C3×D311yescharacteristic
618C2×C8C22×C3×D311yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4C22×C3×D311yescharacteristic
629C22⋊C4—21no—
630C22⋊C4—31no—
631C22⋊C4—31no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C42—31no—
640C42—61no—
641C42—61no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C22×C3×D411yescharacteristic
675C2×D3—21no—
676C2×D3—21no—
677C2×D3C3×#13512yes—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—41no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—81no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4C2×#23711yescharacteristic
697C3×C4#100411yescharacteristic
698C3×C4C2×C3×#4111yescharacteristic
699C3×C4C3×H(5,𝔽2)11yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—21no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707C32#330111yescharacteristic, complemented, Sylow
708C23—21no—
709C23—21no—
710C23—31no—
711C23C3×D3×D411yescharacteristic
712Q8—21no—
713Q8—61no—
714Q8—61no—
715Q8—122no—
716Q8C3×#23712yes—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—42no—
722D4—62no—
723D4—81no—
724D4—122no—
725D4—122no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—42no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—122no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4C3×D3×D411yescharacteristic
744C2×C4C23×C3×D311yescharacteristic
745C8—21no—
746C8—21no—
747C8—61no—
748C8—61no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—62no—
755C2×C3—81no—
756C2×C3—82no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—81no—
761C2×C3—161no—
762C2×C3#559111yescharacteristic
763C2×C3D3×#13511yescharacteristic
764C2×C3#577511yescharacteristic
765C2×C3C3×#54611yescharacteristic
766C2×C3C2×C3×#13511yescharacteristic
767C2×C3C3×#57711yescharacteristic
768D3—22no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—61no—
780C22—61no—
781C22C2×C3×D3×D411yescharacteristic
782C4—21no—
783C4—22no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4C2×C3×#23711yescharacteristic
793C4C3×#100411yescharacteristic
794C3—21no—
795C3#8010311yescharacteristic, direct product factor
796C3C3×#330111yescharacteristic, complemented
797C2—41no—
798C2—62no—
799C2—81no—
800C2—81no—
801C2C3×#559111yescharacteristic
802C2C3×D3×#13511yescharacteristic
803C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#449C2
socleC22×C32C22×D4
hypercenterC3×#449D3
hypocenterC3C3×#3301
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#5831C2semidirect
2. C3×#5614C2semidirect
3. C32×#449C2semidirect
4. C3×#5233C2semidirect
5. C3×#5170C2semidirect
6. C3×Dic3×SD16C2semidirect
7. C3×#5157C2semidirect
8. C3×#5153C2semidirect
9. C3×#5041C2semidirect
10. C3×D3×#103C2semidirect
11. C3×#4796C2semidirect
12. C3×#4777C2semidirect
13. C3×#4768C2semidirect
14. C3×#67⋊C8C2semidirect
15. C3×#4723C2semidirect
17. #80103C3direct (N × H)
63. #5831C2×C3semidirect
64. #5614C2×C3semidirect
73. C3×#449D3semidirect
74. C3×#449C2×C3semidirect
80. #5233C2×C3semidirect
81. #5170C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. #5157C2×C3semidirect
84. #5153C2×C3semidirect
85. #5041C2×C3semidirect
86. D3×#103C2×C3semidirect
87. #4796C2×C3semidirect
88. #4777C2×C3semidirect
89. #4768C2×C3semidirect
90. #67⋊C8C2×C3semidirect
91. #4723C2×C3semidirect
288. #449C3×D3semidirect
707. C32#3301semidirect
795. C3#80103direct (N × H)
796. C3C3×#3301semidirect

Maximal subgroups

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

subgroupindex
C3×#58312
C3×#56142
C32×#4492
C3×#52332
C3×#51702
C3×Dic3×SD162
C3×#51572
C3×#51532
C3×#50412
C3×D3×#1032
C3×#47962
C3×#47772
C3×#47682
C3×#67⋊C82
C3×#47232
C3×#33013
#801033