Finite Group Databasebeta

← C3×#78806 #11887597

Subgroups — C3×#78806 #11887597

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2C3×#5511C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5C3×#5116C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic
7C3×#4970C211yesmaximal, characteristic, complemented
8C3×#4813C211yesmaximal, characteristic, complemented
9C3×#4811C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4795C211yesmaximal, characteristic, complemented
13C3×#4793C211yesmaximal, characteristic, complemented
14C3×#4792C211yesmaximal, characteristic, complemented
15C3×#4790C211yesmaximal, characteristic, complemented
16C3×#3299—31nomaximal
17#78806C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C3×#946—21no—
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944—21no—
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67—21no—
31C3×C4×#67C2211yescharacteristic
32C3×#924—21no—
33C3×#924—21no—
34C3×#924C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C2×C3×Dic12C2211yescharacteristic
37C2×C3×D3×C8C2211yescharacteristic
38C3×#897C2211yescharacteristic
39C3×#896—21no—
40C3×D3×C4⋊C4C2211yescharacteristic
41C3×#889—21no—
42C3×#888C2211yescharacteristic
43C3×#887C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#554—31no—
62C3×D4×Q8—31no—
63Q8×#67C2×C311yescharacteristic
64#5511C2×C311yescharacteristic
65C3×#487—31no—
66C3×#484—31no—
67C3×#484—31no—
68C3×#477—31no—
69C3×#467—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#451—31no—
73C3×#451—31no—
74C3×C4×Q16—31no—
75C3×C8×D4—31no—
76C2×C3×#103—21no—
77C2×C3×#103—31no—
78C2×C3×#103D311yescharacteristic, complemented
79C2×C3×#103C2×C311yescharacteristic, complemented
80#5228C2×C311yescharacteristic, complemented
81#5116C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic
83#4970C2×C311yescharacteristic, complemented
84#4813C2×C311yescharacteristic, complemented
85#4811C2×C311yescharacteristic, complemented
86#4809C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4795C2×C311yescharacteristic, complemented
89#4793C2×C311yescharacteristic, complemented
90#4792C2×C311yescharacteristic, complemented
91#4790C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—22no—
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
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#3299—31noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C22×C311yescharacteristic
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16—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×C4⋊Q8—61no—
160C3×#125—61no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—61no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C4×Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C2×C3×C4⋊C4—21no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4C2×D311yescharacteristic
177C2×C3×C4⋊C4C22×C311yescharacteristic
178#946—21no—
179#946C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181#944—21no—
182#944C22×C311yescharacteristic
183C2×#216C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185C4×#67—21no—
186C4×#67—21no—
187C4×#67C22×C311yescharacteristic
188#924—21no—
189#924—21no—
190#924C22×C311yescharacteristic
191#924C22×C311yescharacteristic
192C2×Dic12C22×C311yescharacteristic
193C2×D3×C8C22×C311yescharacteristic
194#897C22×C311yescharacteristic
195#896—21no—
196D3×C4⋊C4C22×C311yescharacteristic
197#889—21no—
198#888C22×C311yescharacteristic
199#887C22×C311yescharacteristic
200C3×#107—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C2×D311yescharacteristic
217C3×#103C2×D311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×#103C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#835C22×C311yescharacteristic
226#835C22×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#807C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—42no—
244C32×Q8#4112yes—
245C2×C32×C4—21no—
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×C4—81no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67Q1614yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×C4×D3—81no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6—81no—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—31no—
278D4×Q8—31no—
279#487—31no—
280#484—31no—
281#484—31no—
282#477—31no—
283#467—31no—
284#467—31no—
285#462—31no—
286#451—31no—
287#451—31no—
288C4×Q16—31no—
289C8×D4—31no—
290C2×#103—31no—
291C2×#103C3×D311yescharacteristic, complemented
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—24no—
295C2×C3×Q8—22no—
296C2×C3×Q8—22no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8—31no—
301C2×C3×Q8—41no—
302C2×C3×Q8—41no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—61no—
306C2×C3×Q8—61no—
307C2×C3×Q8—62no—
308C2×C3×Q8—121no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C23×C311yescharacteristic
312C2×C3×Q8C23×C311yescharacteristic
313C2×C3×D4—31no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—41no—
321C22×C3×C4—41no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C23×C311yescharacteristic
326C2×#67C3×D411yescharacteristic
327D3×Q8—22no—
328D3×Q8—41no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3C23×C311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—21no—
334C2×Dic6C23×C311yescharacteristic
335C2×Dic6C23×C311yescharacteristic
336C3×Q16—62no—
337C3×Q16—121no—
338C3×Q16—121no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—41no—
344C2×C3×C8—41no—
345C2×C3×C8—42no—
346C2×C3×C8—121no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C2×C3×C8C23×C311yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C23×C311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C22⋊C4—31no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—31no—
380C3×C42—61no—
381C3×C42—61no—
382#217—21no—
383#217—21no—
384#217C3×D411yescharacteristic
385#216—22no—
386#216—41no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4C3×D411yescharacteristic
390C4⋊Dic3—21no—
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⋊C4—21no—
402Dic3⋊C4C3×D411yescharacteristic
403C4×Dic3—21no—
404C4×Dic3—21no—
405C4×Dic3C23×C311yescharacteristic
406C2×C3⋊C8C23×C311yescharacteristic
407C2×C3⋊C8C23×C311yescharacteristic
408Dic12—41no—
409D3×C8—41no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C2×Q1612yes—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3C2×Q1612yes—
417C32×C4—21no—
418C32×C4—22no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3C2×Q1612yes—
431C22×Q8—31no—
432C22×Q8C2×C3×D311yescharacteristic
433C2×Q16—31no—
434C2×Q16—31no—
435C2×Q16—31no—
436C22×C8—31no—
437C22×C8C2×C3×D311yescharacteristic
438C4⋊Q8—31no—
439C4⋊Q8—31no—
440C4⋊Q8—61no—
441#125—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448C22⋊Q8—61no—
449C22⋊Q8—61no—
450C4×Q8—31no—
451C4×Q8—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455C2×C4⋊C4—31no—
456C2×C4⋊C4C2×C3×D311yescharacteristic
457#107—31no—
458#107—31no—
459#107—31no—
460C4⋊C8—31no—
461#103—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#103C2×C3×D311yescharacteristic
470#103C2×C3×D311yescharacteristic
471C22⋊C8—31no—
472C22⋊C8—31no—
473C4×C8—31no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×C3×D411yescharacteristic
478C22×D3C2×C3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—22no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—42no—
490C3×Q8—42no—
491C3×Q8—44no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×Q8—241no—
498C3×Q8#23512yes—
499C3×Q8C3×#4112yes—
500C3×D4—34no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
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—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—42no—
525C2×C3×C4—42no—
526C2×C3×C4—44no—
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—81no—
534C2×C3×C4—81no—
535C2×C3×C4—82no—
536C2×C3×C4—122no—
537C2×C3×C4—241no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C24×C311yescharacteristic
542#67C3×Q1614yescomplemented
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—42no—
553C4×D3—81no—
554Dic6—21no—
555Dic6—21no—
556Dic6—21no—
557Dic6—21no—
558Dic6—42no—
559Dic6—81no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C2×C32—22no—
571C2×C32#54611yescharacteristic
572C2×C32C22×Q1611yescharacteristic
573C2×C32#57711yescharacteristic
574C3×D3—22no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—31no—
578C2×Q8—31no—
579C2×Q8—41no—
580C2×Q8—61no—
581C2×Q8—61no—
582C2×Q8—62no—
583C2×Q8—121no—
584C2×Q8C22×C3×D311yescharacteristic
585C2×Q8C22×C3×D311yescharacteristic
586C2×D4—31no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4C22×C3×D311yescharacteristic
593Q16—62no—
594Q16—121no—
595Q16—121no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—41no—
599C2×C8—121no—
600C2×C8C22×C3×D311yescharacteristic
601C2×C8C22×C3×D311yescharacteristic
602C4⋊C4—21no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C42—31no—
625C42—61no—
626C42—61no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3D3×Q1612yes—
639C22×C3C2×C3×Q1612yes—
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C22×C3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3C2×C3×Q1612yes—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—32no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4C2×#23511yescharacteristic
670C3×C4#100411yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672C3×C4C3×H(5,𝔽2)11yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3C2×C3×Q1612yes—
680C32#329911yescharacteristic, complemented, Sylow
681C23—31no—
682C23C3×D3×D411yescharacteristic
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—42no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—61no—
691Q8—122no—
692Q8—241no—
693Q8C3×#23512yes—
694D4—34no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—81no—
712C2×C4—122no—
713C2×C4—241no—
714C2×C4C3×D3×D411yescharacteristic
715C2×C4C23×C3×D311yescharacteristic
716C8—21no—
717C8—21no—
718C8—61no—
719C8—61no—
720C2×C3—24no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—62no—
727C2×C3#549011yescharacteristic
728C2×C3#576211yescharacteristic
729C2×C3C2×D3×Q1611yescharacteristic
730C2×C3C3×#54611yescharacteristic
731C2×C3C22×C3×Q1611yescharacteristic
732C2×C3C3×#57711yescharacteristic
733D3—22no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22C3×D3×Q1612yes—
740C22C2×C3×D3×D411yescharacteristic
741C4—21no—
742C4—22no—
743C4—32no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4C2×C3×#23511yescharacteristic
754C4C3×#100411yescharacteristic
755C3—21no—
756C3#7880611yescharacteristic, direct product factor
757C3C3×#329911yescharacteristic, complemented
758C2—22no—
759C2—62no—
760C2C3×#549011yescharacteristic
761C2C3×#576211yescharacteristic
762C2C2×C3×D3×Q1611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#103C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC2×C3×#103D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
3. C2×C32×#103C2semidirect
4. C3×#5228C2semidirect
5. C3×#5116C2semidirect
7. C3×#4970C2semidirect
8. C3×#4813C2semidirect
9. C3×#4811C2semidirect
10. C3×#4809C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4795C2semidirect
13. C3×#4793C2semidirect
14. C3×#4792C2semidirect
15. C3×#4790C2semidirect
17. #78806C3direct (N × H)
78. C2×C3×#103D3semidirect
79. C2×C3×#103C2×C3semidirect
80. #5228C2×C3semidirect
81. #5116C2×C3semidirect
83. #4970C2×C3semidirect
84. #4813C2×C3semidirect
85. #4811C2×C3semidirect
86. #4809C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4795C2×C3semidirect
89. #4793C2×C3semidirect
90. #4792C2×C3semidirect
91. #4790C2×C3semidirect
255. C3×#67Q16semidirect
291. C2×#103C3×D3semidirect
542. #67C3×Q16semidirect
680. C32#3299semidirect
756. C3#78806direct (N × H)
757. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C3×#55112
C2×C32×#1032
C3×#52282
C3×#51162
C3×C8×#672
C3×#49702
C3×#48132
C3×#48112
C3×#48092
C3×D3×#1032
C3×#47952
C3×#47932
C3×#47922
C3×#47902
C3×#32993
#788063