Finite Group Databasebeta

← C2×C61×#3388 #29564795

Subgroups — C2×C61×#3388 #29564795

Order 15616.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#557C211yesmaximal, characteristic, complemented
2C2×C61×#554C211yesmaximal, characteristic
3C61×#3388C2116yesmaximal, direct product factor
4C2×C61×#501C211yesmaximal, characteristic, complemented
5C2×C61×#501C211yesmaximal, characteristic, complemented
6C2×C61×#499C211yesmaximal, characteristic, complemented
7C2×C61×#479C211yesmaximal, characteristic, complemented
8C2×C61×#479C211yesmaximal, characteristic, complemented
9C2×C61×#475C211yesmaximal, characteristic, complemented
10C2×C61×#478C211yesmaximal, characteristic
11C2×C61×#478C211yesmaximal, characteristic
12C2×C61×#476C211yesmaximal, characteristic
13C2×C61×#446C211yesmaximal, characteristic, complemented
14C2×C61×#440C211yesmaximal, characteristic
15C2×C61×#440C211yesmaximal, characteristic
16C2×C4×SD16×C61C211yesmaximal, characteristic
17C22×SD16×C61C2211yescharacteristic
18C61×#557—24no—
19C61×#557C2218yescomplemented
20C61×#554—24no—
21C61×#554C2218yes—
22C2×C4⋊Q8×C61—21no—
23C2×C4⋊Q8×C61C2211yescharacteristic
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#125×C61—21no—
26C2×#125×C61—21no—
27C2×#125×C61C2211yescharacteristic
28C2×#125×C61C2211yescharacteristic
29C2×#125×C61C2211yescharacteristic
30C2×#125×C61C2211yescharacteristic
31C2×C22⋊Q8×C61—21no—
32C2×C22⋊Q8×C61—21no—
33C2×C22⋊Q8×C61—21no—
34C2×C4×Q8×C61—21no—
35C2×C4×Q8×C61C2211yescharacteristic
36C2×C4×Q8×C61C2211yescharacteristic
37C2×C4×Q8×C61C2211yescharacteristic
38C2×C4×Q8×C61C2211yescharacteristic
39C2×C4×D4×C61C2211yescharacteristic
40C2×C4×D4×C61C2211yescharacteristic
41C2×C4×D4×C61C2211yescharacteristic
42C22×C4⋊C4×C61—21no—
43C61×#501C2218yescomplemented
44C61×#501C2218yescomplemented
45C61×#499C2218yescomplemented
46C61×#479C2218yescomplemented
47C61×#479C2218yescomplemented
48C61×#478C2218yes—
49C61×#478C2218yes—
50C61×#476C2218yes—
51C61×#475C2218yescomplemented
52C61×#446C2218yescomplemented
53C61×#440C2218yes—
54C61×#440C2218yes—
55C4×SD16×C61C2218yes—
56C2×#107×C61C2211yescharacteristic
57C2×#107×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#107×C61C2211yescharacteristic
60C2×#106×C61C2211yescharacteristic
61C2×#106×C61C2211yescharacteristic
62C2×#106×C61C2211yescharacteristic
63C2×#106×C61C2211yescharacteristic
64C2×#106×C61C2211yescharacteristic
65C2×C4⋊C8×C61C2211yescharacteristic
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×C4⋊C8×C61C2211yescharacteristic
68C2×#103×C61C2211yescharacteristic
69C2×#103×C61C2211yescharacteristic
70C2×#103×C61C2211yescharacteristic
71C2×#102×C61C2211yescharacteristic
72C2×#102×C61C2211yescharacteristic
73C2×#102×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic
75C2×#97×C61C2211yescharacteristic
76C2×C4×C8×C61C2211yescharacteristic
77C22×Q8×C61—21no—
78C22×Q8×C61—21no—
79C22×Q8×C61D411yescharacteristic
80C22×Q8×C61C2311yescharacteristic
81C22×D4×C61C2311yescharacteristic
82C23×C4×C61—21no—
83C23×C4×C61—21no—
84C23×C4×C61—21no—
85C2×SD16×C61Q818yescomplemented
86C2×SD16×C61C2314yes—
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91C4⋊Q8×C61—28no—
92C4⋊Q8×C61—22no—
93C4⋊Q8×C61—22no—
94C4⋊Q8×C61C2314yes—
95C4⋊Q8×C61C2314yes—
96#125×C61—28no—
97#125×C61—28no—
98#125×C61—22no—
99#125×C61—22no—
100#125×C61—22no—
101#125×C61—22no—
102#125×C61C2314yes—
103#125×C61C2314yes—
104#125×C61C2314yes—
105#125×C61C2314yes—
106C22⋊Q8×C61—28no—
107C22⋊Q8×C61—28no—
108C22⋊Q8×C61—28no—
109C4×Q8×C61—28no—
110C4×Q8×C61—22no—
111C4×Q8×C61—22no—
112C4×Q8×C61—22no—
113C4×Q8×C61D414yes—
114C4×Q8×C61C2314yes—
115C4×Q8×C61C2314yes—
116C4×Q8×C61C2314yes—
117C4×Q8×C61C2314yes—
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120C4×D4×C61—22no—
121C4×D4×C61C2314yes—
122C4×D4×C61C2314yes—
123C4×D4×C61C2314yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61—28no—
138C2×C4⋊C4×C61D411yescharacteristic
139C2×C4⋊C4×C61D411yescharacteristic
140C2×C4⋊C4×C61D411yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C42×C61—21no—
151C2×C42×C61—21no—
152C2×C42×C61—21no—
153C2×C42×C61C2311yescharacteristic
154C2×C42×C61C2311yescharacteristic
155C2×C42×C61C2311yescharacteristic
156#107×C61C2314yes—
157#107×C61C2314yes—
158#107×C61C2314yes—
159#107×C61C2314yes—
160#106×C61C2314yes—
161#106×C61C2314yes—
162#106×C61C2314yes—
163#106×C61C2314yes—
164#106×C61C2314yes—
165C4⋊C8×C61C2314yes—
166C4⋊C8×C61C2314yes—
167C4⋊C8×C61C2314yes—
168#103×C61C2314yes—
169#103×C61C2314yes—
170#103×C61C2314yes—
171#102×C61C2314yes—
172#102×C61C2314yes—
173#102×C61C2314yes—
174#97×C61C2314yes—
175#97×C61C2314yes—
176C4×C8×C61C2314yes—
177C24×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—24no—
180C2×Q8×C61—24no—
181C2×Q8×C61—22no—
182C2×Q8×C61—42no—
183C2×Q8×C61—44no—
184C2×Q8×C61—82no—
185C2×Q8×C61C2×D414yes—
186C2×Q8×C61C2×Q814yes—
187C2×Q8×C61C2412yes—
188C2×D4×C61—21no—
189C2×D4×C61—22no—
190C2×D4×C61C2×Q814yes—
191C2×D4×C61C2412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—24no—
200C22×C4×C61—24no—
201C22×C4×C61—24no—
202C22×C4×C61—44no—
203C22×C4×C61—82no—
204C22×C4×C61—82no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2411yescharacteristic
212SD16×C61C2×Q8116yescomplemented
213C2×C8×C61—22no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61C2×Q814yes—
217C2×C8×C61C2412yes—
218C2×C8×C61C2412yes—
219C2×C8×C61C2412yes—
220C2×C8×C61C2412yes—
221C4⋊C4×C61—24no—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—24no—
228C4⋊C4×C61—24no—
229C4⋊C4×C61—24no—
230C4⋊C4×C61—24no—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—24no—
233C4⋊C4×C61—24no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C2×D414yes—
241C4⋊C4×C61C2×D414yes—
242C4⋊C4×C61C2×D414yes—
243C4⋊C4×C61C2412yes—
244C4⋊C4×C61C2412yes—
245C4⋊C4×C61C2412yes—
246C4⋊C4×C61C2412yes—
247C4⋊C4×C61C2412yes—
248C4⋊C4×C61C2412yes—
249C22⋊C4×C61—24no—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C42×C61—24no—
253C42×C61—24no—
254C42×C61—24no—
255C42×C61C2×D412yes—
256C42×C61C2×D412yes—
257C42×C61C2×D412yes—
258C42×C61C2412yes—
259C42×C61C2412yes—
260C42×C61C2412yes—
261C23×C61—24no—
262C23×C61—22no—
263C23×C61—42no—
264C23×C61—42no—
265C23×C61C22×D411yescharacteristic
266Q8×C61—24no—
267Q8×C61—22no—
268Q8×C61—44no—
269Q8×C61—48no—
270Q8×C61—84no—
271Q8×C61C22×Q814yes—
272D4×C61—24no—
273D4×C61—22no—
274D4×C61C22×Q814yes—
275C2×C4×C61—24no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—48no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—42no—
295C2×C4×C61—42no—
296C2×C4×C61—84no—
297C2×C4×C61—84no—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D412yes—
300C2×C4×C61C22×D412yes—
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D412yes—
303C2×C4×C61C22×D412yes—
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C22×Q812yes—
306C2×C4×C612−1+412yes—
307C2×C4×C61C2511yescharacteristic
308C8×C61—22no—
309C8×C61—22no—
310C8×C61—22no—
311C8×C61C22×Q814yes—
312C2×#3388C6111yesmaximal, characteristic, direct product factor, Sylow
313C22×C61—24no—
314C22×C61—48no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61D4×Q812yes—
318C22×C61#57512yes—
319C22×C61#57712yes—
320C22×C61C23×D411yescharacteristic
321C4×C61—24no—
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—22no—
325C4×C61—22no—
326C4×C61—22no—
327C4×C61—22no—
328C4×C61—42no—
329C4×C61—42no—
330C4×C61—42no—
331C4×C61—42no—
332C4×C61—42no—
333C4×C61—42no—
334C4×C61D4×Q812yes—
335C4×C61C23×Q811yescharacteristic
336C4×C61C2×2−1+411yescharacteristic
337C2×#557C2×C6111yescharacteristic, complemented
338C2×#554C2×C6111yescharacteristic
339#3388C2×C61116yesdirect product factor
340C2×#501C2×C6111yescharacteristic, complemented
341C2×#501C2×C6111yescharacteristic, complemented
342C2×#499C2×C6111yescharacteristic, complemented
343C2×#479C2×C6111yescharacteristic, complemented
344C2×#479C2×C6111yescharacteristic, complemented
345C2×#475C2×C6111yescharacteristic, complemented
346C2×#478C2×C6111yescharacteristic
347C2×#478C2×C6111yescharacteristic
348C2×#476C2×C6111yescharacteristic
349C2×#446C2×C6111yescharacteristic, complemented
350C2×#440C2×C6111yescharacteristic
351C2×#440C2×C6111yescharacteristic
352C2×C4×SD16C2×C6111yescharacteristic
353C2×C61—44no—
354C2×C61#338814yesdirect product factor
355C2×C61C2×D4×Q811yescharacteristic
356C2×C61C2×#57511yescharacteristic
357C2×C61C2×#57711yescharacteristic
358C22×SD16C22×C6111yescharacteristic
359#557—24no—
360#557C22×C6118yescomplemented
361#554—24no—
362#554C22×C6118yes—
363C2×C4⋊Q8—21no—
364C2×C4⋊Q8C22×C6111yescharacteristic
365C2×C4⋊Q8C22×C6111yescharacteristic
366C2×#125—21no—
367C2×#125—21no—
368C2×#125C22×C6111yescharacteristic
369C2×#125C22×C6111yescharacteristic
370C2×#125C22×C6111yescharacteristic
371C2×#125C22×C6111yescharacteristic
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C4×Q8—21no—
376C2×C4×Q8C22×C6111yescharacteristic
377C2×C4×Q8C22×C6111yescharacteristic
378C2×C4×Q8C22×C6111yescharacteristic
379C2×C4×Q8C22×C6111yescharacteristic
380C2×C4×D4C22×C6111yescharacteristic
381C2×C4×D4C22×C6111yescharacteristic
382C2×C4×D4C22×C6111yescharacteristic
383C22×C4⋊C4—21no—
384#501C22×C6118yescomplemented
385#501C22×C6118yescomplemented
386#499C22×C6118yescomplemented
387#479C22×C6118yescomplemented
388#479C22×C6118yescomplemented
389#478C22×C6118yes—
390#478C22×C6118yes—
391#476C22×C6118yes—
392#475C22×C6118yescomplemented
393#446C22×C6118yescomplemented
394#440C22×C6118yes—
395#440C22×C6118yes—
396C4×SD16C22×C6118yes—
397C2×#107C22×C6111yescharacteristic
398C2×#107C22×C6111yescharacteristic
399C2×#107C22×C6111yescharacteristic
400C2×#107C22×C6111yescharacteristic
401C2×#106C22×C6111yescharacteristic
402C2×#106C22×C6111yescharacteristic
403C2×#106C22×C6111yescharacteristic
404C2×#106C22×C6111yescharacteristic
405C2×#106C22×C6111yescharacteristic
406C2×C4⋊C8C22×C6111yescharacteristic
407C2×C4⋊C8C22×C6111yescharacteristic
408C2×C4⋊C8C22×C6111yescharacteristic
409C2×#103C22×C6111yescharacteristic
410C2×#103C22×C6111yescharacteristic
411C2×#103C22×C6111yescharacteristic
412C2×#102C22×C6111yescharacteristic
413C2×#102C22×C6111yescharacteristic
414C2×#102C22×C6111yescharacteristic
415C2×#97C22×C6111yescharacteristic
416C2×#97C22×C6111yescharacteristic
417C2×C4×C8C22×C6111yescharacteristic
418C61C2×#338811yescharacteristic, direct product factor, Sylow
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8D4×C6111yescharacteristic
422C22×Q8C23×C6111yescharacteristic
423C22×D4C23×C6111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16Q8×C6118yescomplemented
428C2×SD16C23×C6114yes—
429C22×C8C23×C6111yescharacteristic
430C22×C8C23×C6111yescharacteristic
431C22×C8C23×C6111yescharacteristic
432C22×C8C23×C6111yescharacteristic
433C4⋊Q8—28no—
434C4⋊Q8—22no—
435C4⋊Q8—22no—
436C4⋊Q8C23×C6114yes—
437C4⋊Q8C23×C6114yes—
438#125—28no—
439#125—28no—
440#125—22no—
441#125—22no—
442#125—22no—
443#125—22no—
444#125C23×C6114yes—
445#125C23×C6114yes—
446#125C23×C6114yes—
447#125C23×C6114yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—28no—
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455C4×Q8D4×C6114yes—
456C4×Q8C23×C6114yes—
457C4×Q8C23×C6114yes—
458C4×Q8C23×C6114yes—
459C4×Q8C23×C6114yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C23×C6114yes—
464C4×D4C23×C6114yes—
465C4×D4C23×C6114yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—28no—
480C2×C4⋊C4D4×C6111yescharacteristic
481C2×C4⋊C4D4×C6111yescharacteristic
482C2×C4⋊C4D4×C6111yescharacteristic
483C2×C4⋊C4C23×C6111yescharacteristic
484C2×C4⋊C4C23×C6111yescharacteristic
485C2×C4⋊C4C23×C6111yescharacteristic
486C2×C4⋊C4C23×C6111yescharacteristic
487C2×C4⋊C4C23×C6111yescharacteristic
488C2×C4⋊C4C23×C6111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C23×C6111yescharacteristic
496C2×C42C23×C6111yescharacteristic
497C2×C42C23×C6111yescharacteristic
498#107C23×C6114yes—
499#107C23×C6114yes—
500#107C23×C6114yes—
501#107C23×C6114yes—
502#106C23×C6114yes—
503#106C23×C6114yes—
504#106C23×C6114yes—
505#106C23×C6114yes—
506#106C23×C6114yes—
507C4⋊C8C23×C6114yes—
508C4⋊C8C23×C6114yes—
509C4⋊C8C23×C6114yes—
510#103C23×C6114yes—
511#103C23×C6114yes—
512#103C23×C6114yes—
513#102C23×C6114yes—
514#102C23×C6114yes—
515#102C23×C6114yes—
516#97C23×C6114yes—
517#97C23×C6114yes—
518C4×C8C23×C6114yes—
519C24—21no—
520C2×Q8—21no—
521C2×Q8—24no—
522C2×Q8—24no—
523C2×Q8—22no—
524C2×Q8—42no—
525C2×Q8—44no—
526C2×Q8—82no—
527C2×Q8C2×D4×C6114yes—
528C2×Q8C2×Q8×C6114yes—
529C2×Q8C24×C6112yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4C2×Q8×C6114yes—
533C2×D4C24×C6112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—44no—
545C22×C4—82no—
546C22×C4—82no—
547C22×C4C2×D4×C6111yescharacteristic
548C22×C4C2×D4×C6111yescharacteristic
549C22×C4C2×D4×C6111yescharacteristic
550C22×C4C2×D4×C6111yescharacteristic
551C22×C4C2×D4×C6111yescharacteristic
552C22×C4C2×D4×C6111yescharacteristic
553C22×C4C24×C6111yescharacteristic
554SD16C2×Q8×C61116yescomplemented
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8C2×Q8×C6114yes—
559C2×C8C24×C6112yes—
560C2×C8C24×C6112yes—
561C2×C8C24×C6112yes—
562C2×C8C24×C6112yes—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4C2×D4×C6114yes—
583C4⋊C4C2×D4×C6114yes—
584C4⋊C4C2×D4×C6114yes—
585C4⋊C4C24×C6112yes—
586C4⋊C4C24×C6112yes—
587C4⋊C4C24×C6112yes—
588C4⋊C4C24×C6112yes—
589C4⋊C4C24×C6112yes—
590C4⋊C4C24×C6112yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—24no—
595C42—24no—
596C42—24no—
597C42C2×D4×C6112yes—
598C42C2×D4×C6112yes—
599C42C2×D4×C6112yes—
600C42C24×C6112yes—
601C42C24×C6112yes—
602C42C24×C6112yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×D4×C6111yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—84no—
613Q8C22×Q8×C6114yes—
614D4—24no—
615D4—22no—
616D4C22×Q8×C6114yes—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—48no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4C22×D4×C6112yes—
641C2×C4C22×D4×C6112yes—
642C2×C4C22×D4×C6112yes—
643C2×C4C22×D4×C6112yes—
644C2×C4C22×D4×C6112yes—
645C2×C4C22×D4×C6112yes—
646C2×C4C22×D4×C6111yescharacteristic
647C2×C4C22×Q8×C6112yes—
648C2×C42−1+4×C6112yes—
649C2×C4C25×C6111yescharacteristic
650C8—22no—
651C8—22no—
652C8—22no—
653C8C22×Q8×C6114yes—
654C22—24no—
655C22—42no—
656C22—42no—
657C22—48no—
658C22D4×Q8×C6112yes—
659C22C61×#57512yes—
660C22C61×#57712yes—
661C22C23×D4×C6111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—24no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4D4×Q8×C6112yes—
676C4C23×Q8×C6111yescharacteristic
677C4C2×2−1+4×C6111yescharacteristic
678C2—44no—
679C2C61×#338814yesdirect product factor
680C2C2×D4×Q8×C6111yescharacteristic
681C2C2×C61×#57511yescharacteristic
682C2C2×C61×#57711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC22×D4×C61C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#557C2semidirect
3. C61×#3388C2direct (N × H)
4. C2×C61×#501C2semidirect
5. C2×C61×#501C2semidirect
6. C2×C61×#499C2semidirect
7. C2×C61×#479C2semidirect
8. C2×C61×#479C2semidirect
9. C2×C61×#475C2semidirect
13. C2×C61×#446C2semidirect
19. C61×#557C22semidirect
43. C61×#501C22semidirect
44. C61×#501C22semidirect
45. C61×#499C22semidirect
46. C61×#479C22semidirect
47. C61×#479C22semidirect
51. C61×#475C22semidirect
52. C61×#446C22semidirect
85. C2×SD16×C61Q8semidirect
212. SD16×C61C2×Q8semidirect
312. C2×#3388C61direct (N × H)
337. C2×#557C2×C61semidirect
339. #3388C2×C61direct (N × H)
340. C2×#501C2×C61semidirect
341. C2×#501C2×C61semidirect
342. C2×#499C2×C61semidirect
343. C2×#479C2×C61semidirect
344. C2×#479C2×C61semidirect
345. C2×#475C2×C61semidirect
349. C2×#446C2×C61semidirect
354. C2×C61#3388direct (N × H)
360. #557C22×C61semidirect
384. #501C22×C61semidirect
385. #501C22×C61semidirect
386. #499C22×C61semidirect
387. #479C22×C61semidirect
388. #479C22×C61semidirect
392. #475C22×C61semidirect
393. #446C22×C61semidirect
418. C61C2×#3388direct (N × H)
427. C2×SD16Q8×C61semidirect
554. SD16C2×Q8×C61semidirect
679. C2C61×#3388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5572
C2×C61×#5542
C61×#33882
C2×C61×#5012
C2×C61×#4992
C2×C61×#4792
C2×C61×#4752
C2×C61×#4782
C2×C61×#4762
C2×C61×#4462
C2×C61×#4402
C2×C4×SD16×C612
C2×#338861