Finite Group Databasebeta

← C2×C107×#2009 #41049375

Subgroups — C2×C107×#2009 #41049375

Order 27392.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C107C211yesmaximal, characteristic
2C22×#137×C107C211yesmaximal, characteristic, complemented
3C2×#536×C107C211yesmaximal, characteristic, complemented
4C2×#421×C107C211yesmaximal, characteristic, complemented
5C2×#419×C107C211yesmaximal, characteristic, complemented
6C2×#410×C107C211yesmaximal, characteristic, complemented
7C107×#2009C218yesmaximal, direct product factor
8C2×#344×C107C211yesmaximal, characteristic, complemented
9C22×#41×C107C2211yescharacteristic
10C22×#41×C107C2211yescharacteristic
11C23×Q8×C107C2211yescharacteristic
12#575×C107—22no—
13#575×C107—22no—
14#575×C107—22no—
15#575×C107C2214yes—
16C2×#137×C107—22no—
17C2×#137×C107—22no—
18C2×#137×C107—22no—
19C2×#137×C107—21no—
20C2×#137×C107—21no—
21C2×#137×C107—22no—
22C2×#137×C107—22no—
23C2×#137×C107C2214yescomplemented
24C2×AGL(1,ℤ/8)×C107—21no—
25C2×AGL(1,ℤ/8)×C107—21no—
26C2×#135×C107—22no—
27C22×Q16×C107—21no—
28C22×SD16×C107—21no—
29C22×M16×C107C2211yescharacteristic
30C22×M16×C107C2211yescharacteristic
31#536×C107—22no—
32#536×C107—22no—
33#536×C107—22no—
34#536×C107C2214yescomplemented
35C2×C4⋊Q8×C107—21no—
36C2×#124×C107—21no—
37C2×#123×C107—22no—
38C2×C22⋊Q8×C107—22no—
39C2×#117×C107C2211yescharacteristic
40C2×#117×C107C2211yescharacteristic
41#421×C107—22no—
42#421×C107C2214yescomplemented
43C2×#104×C107—22no—
44#419×C107—22no—
45#419×C107C2214yescomplemented
46C2×#103×C107—22no—
47#410×C107—22no—
48#410×C107C2214yescomplemented
49C2×#99×C107—22no—
50#344×C107C2214yescomplemented
51C2×#41×C107—21no—
52C2×#41×C107—21no—
53C2×#41×C107—21no—
54C2×#41×C107—21no—
55C2×#41×C107—21no—
56C2×#41×C107—21no—
57C2×#41×C107—21no—
58C2×#41×C107—21no—
59C2×#41×C107—21no—
60C2×#41×C107—21no—
61C2×#41×C107—21no—
62C2×#41×C107—21no—
63C2×#41×C107—21no—
64C2×#41×C107—21no—
65C2×#41×C107—21no—
66C2×#41×C107—21no—
67C2×#41×C107—21no—
68C2×#41×C107—21no—
69C2×#41×C107—21no—
70C2×#41×C107—21no—
71C2×#41×C107D412yes—
72C2×#41×C107D412yes—
73C2×#41×C107C2312yes—
74C2×#41×C107C2312yes—
75C22×Q8×C107—21no—
76C22×Q8×C107—21no—
77C22×Q8×C107—21no—
78C22×Q8×C107—21no—
79C22×Q8×C107—21no—
80C22×Q8×C107—21no—
81C22×Q8×C107—21no—
82C22×Q8×C107—21no—
83C22×Q8×C107—21no—
84C22×Q8×C107—21no—
85C22×Q8×C107—21no—
86C22×Q8×C107D412yes—
87C22×Q8×C107D411yescharacteristic
88C22×Q8×C107D412yes—
89C22×Q8×C107D411yescharacteristic
90C22×Q8×C107C2312yes—
91C22×D4×C107—21no—
92C22×D4×C107—21no—
93C22×D4×C107D411yescharacteristic
94C22×D4×C107D411yescharacteristic
95C23×C4×C107—21no—
96C23×C4×C107—21no—
97C23×C4×C107—21no—
98C23×C4×C107C2311yescharacteristic
99#137×C107—28no—
100#137×C107—28no—
101#137×C107—24no—
102#137×C107—24no—
103#137×C107—28no—
104#137×C107—24no—
105#137×C107—24no—
106#137×C107—28no—
107AGL(1,ℤ/8)×C107—24no—
108AGL(1,ℤ/8)×C107—24no—
109AGL(1,ℤ/8)×C107—24no—
110AGL(1,ℤ/8)×C107—24no—
111#135×C107—28no—
112#135×C107—28no—
113C2×Q16×C107—24no—
114C2×Q16×C107—24no—
115C2×Q16×C107—22no—
116C2×Q16×C107—24no—
117C2×SD16×C107—24no—
118C2×SD16×C107—24no—
119C2×SD16×C107—22no—
120C2×SD16×C107—22no—
121C2×SD16×C107—24no—
122C2×D8×C107—22no—
123C2×M16×C107—21no—
124C2×M16×C107—21no—
125C2×M16×C107—21no—
126C2×M16×C107—21no—
127C2×M16×C107—21no—
128C2×M16×C107—21no—
129C2×M16×C107—21no—
130C2×M16×C107D412yes—
131C2×M16×C107D412yes—
132C2×M16×C107D412yes—
133C2×M16×C107C2312yes—
134C2×M16×C107C2312yes—
135C22×C8×C107—21no—
136C22×C8×C107D412yes—
137C4⋊Q8×C107—24no—
138C4⋊Q8×C107—24no—
139#124×C107—24no—
140#124×C107—24no—
141#123×C107—28no—
142#123×C107—28no—
143C22⋊Q8×C107—28no—
144C22⋊Q8×C107—28no—
145#117×C107—21no—
146#117×C107—21no—
147#117×C107—21no—
148#117×C107—21no—
149#117×C107—21no—
150#117×C107D412yes—
151#117×C107C2312yes—
152#117×C107C2312yes—
153C2×C4⋊C4×C107—24no—
154C2×C4⋊C4×C107—21no—
155C2×C4⋊C4×C107—21no—
156C2×C22⋊C4×C107—24no—
157C2×C22⋊C4×C107—21no—
158C2×C22⋊C4×C107D412yes—
159C2×C42×C107—21no—
160C2×C42×C107—21no—
161#104×C107—28no—
162#103×C107—28no—
163#99×C107—28no—
164C24×C107—21no—
165C24×C107—21no—
166C24×C107C2×D411yescharacteristic
167#41×C107—22no—
168#41×C107—22no—
169#41×C107—22no—
170#41×C107—22no—
171#41×C107—22no—
172#41×C107—22no—
173#41×C107—22no—
174#41×C107—22no—
175#41×C107—22no—
176#41×C107—22no—
177#41×C107—22no—
178#41×C107—22no—
179#41×C107—22no—
180#41×C107—22no—
181#41×C107—22no—
182#41×C107—22no—
183#41×C107—41no—
184#41×C107—41no—
185#41×C107—41no—
186#41×C107—41no—
187#41×C107—41no—
188#41×C107—41no—
189#41×C107—41no—
190#41×C107—41no—
191#41×C107—41no—
192#41×C107—41no—
193#41×C107—41no—
194#41×C107—41no—
195#41×C107—41no—
196#41×C107—41no—
197#41×C107—41no—
198#41×C107—41no—
199C2×Q8×C107—22no—
200C2×Q8×C107—22no—
201C2×Q8×C107—21no—
202C2×Q8×C107—21no—
203C2×Q8×C107—22no—
204C2×Q8×C107—22no—
205C2×Q8×C107—22no—
206C2×Q8×C107—21no—
207C2×Q8×C107—21no—
208C2×Q8×C107—21no—
209C2×Q8×C107—21no—
210C2×Q8×C107—22no—
211C2×Q8×C107—22no—
212C2×Q8×C107—21no—
213C2×Q8×C107—21no—
214C2×Q8×C107—22no—
215C2×Q8×C107—22no—
216C2×Q8×C107—22no—
217C2×Q8×C107—22no—
218C2×Q8×C107—21no—
219C2×Q8×C107—21no—
220C2×Q8×C107—22no—
221C2×Q8×C107—22no—
222C2×Q8×C107—22no—
223C2×Q8×C107—22no—
224C2×Q8×C107—41no—
225C2×Q8×C107—41no—
226C2×Q8×C107—41no—
227C2×Q8×C107—41no—
228C2×Q8×C107—41no—
229C2×Q8×C107—41no—
230C2×Q8×C107—41no—
231C2×Q8×C107—41no—
232C2×Q8×C107—41no—
233C2×Q8×C107—41no—
234C2×Q8×C107—41no—
235C2×Q8×C107—41no—
236C2×Q8×C107C2×D414yes—
237C2×Q8×C107C2×D412yes—
238C2×Q8×C107C2×D412yes—
239C2×D4×C107—22no—
240C2×D4×C107—22no—
241C2×D4×C107—22no—
242C2×D4×C107—22no—
243C2×D4×C107—21no—
244C2×D4×C107—21no—
245C2×D4×C107—21no—
246C2×D4×C107—21no—
247C2×D4×C107—21no—
248C2×D4×C107—21no—
249C2×D4×C107—21no—
250C2×D4×C107—21no—
251C2×D4×C107—21no—
252C2×D4×C107—21no—
253C2×D4×C107—41no—
254C2×D4×C107—41no—
255C2×D4×C107—41no—
256C2×D4×C107—41no—
257C2×D4×C107—41no—
258C2×D4×C107—41no—
259C2×D4×C107—41no—
260C2×D4×C107—41no—
261C2×D4×C107C2×D412yes—
262C2×D4×C107C2×D412yes—
263C22×C4×C107—22no—
264C22×C4×C107—22no—
265C22×C4×C107—21no—
266C22×C4×C107—22no—
267C22×C4×C107—21no—
268C22×C4×C107—22no—
269C22×C4×C107—22no—
270C22×C4×C107—22no—
271C22×C4×C107—22no—
272C22×C4×C107—22no—
273C22×C4×C107—41no—
274C22×C4×C107—41no—
275C22×C4×C107—41no—
276C22×C4×C107—41no—
277C22×C4×C107—41no—
278C22×C4×C107—41no—
279C22×C4×C107—41no—
280C22×C4×C107—41no—
281C22×C4×C107—41no—
282C22×C4×C107—41no—
283C22×C4×C107—41no—
284C22×C4×C107—41no—
285C22×C4×C107—41no—
286C22×C4×C107C2×D411yescharacteristic
287C22×C4×C107C2×D411yescharacteristic
288C22×C4×C107C2×D411yescharacteristic
289C22×C4×C107C2×D411yescharacteristic
290C22×C4×C107C2×D411yescharacteristic
291C22×C4×C107C2×D411yescharacteristic
292C22×C4×C107C2×D411yescharacteristic
293C22×C4×C107C2×D411yescharacteristic
294C22×C4×C107C2×D411yescharacteristic
295C22×C4×C107C2×D411yescharacteristic
296C22×C4×C107C2×D411yescharacteristic
297C22×C4×C107#4111yescharacteristic
298C22×C4×C107#4111yescharacteristic
299C22×C4×C107C2411yescharacteristic
300Q16×C107—216no—
301Q16×C107—28no—
302SD16×C107—216no—
303SD16×C107—28no—
304SD16×C107—28no—
305D8×C107—28no—
306M16×C107—22no—
307M16×C107—22no—
308M16×C107—22no—
309M16×C107—22no—
310M16×C107—22no—
311M16×C107—22no—
312M16×C107—22no—
313M16×C107C2×D414yes—
314C2×C8×C107—22no—
315C2×C8×C107—22no—
316C2×C8×C107—22no—
317C2×C8×C107—22no—
318C2×C8×C107—22no—
319C2×C8×C107C2×D414yes—
320C4⋊C4×C107—216no—
321C4⋊C4×C107—22no—
322C4⋊C4×C107—22no—
323C4⋊C4×C107—22no—
324C4⋊C4×C107—41no—
325C22⋊C4×C107—216no—
326C22⋊C4×C107—22no—
327C22⋊C4×C107—22no—
328C22⋊C4×C107—41no—
329C22⋊C4×C107C2×D414yes—
330C42×C107—22no—
331C42×C107—22no—
332C42×C107—22no—
333C42×C107—41no—
334C23×C107—22no—
335C23×C107—22no—
336C23×C107—42no—
337C23×C107—44no—
338C23×C107—41no—
339C23×C107—41no—
340C23×C107—41no—
341C23×C107—41no—
342C23×C107—82no—
343C23×C107#12011yescharacteristic
344C23×C107#12011yescharacteristic
345C23×C107#12111yescharacteristic
346C23×C107#12111yescharacteristic
347C23×C107#12711yescharacteristic
348C23×C107#12711yescharacteristic
349C23×C107C22×D411yescharacteristic
350Q8×C107—24no—
351Q8×C107—22no—
352Q8×C107—22no—
353Q8×C107—22no—
354Q8×C107—24no—
355Q8×C107—22no—
356Q8×C107—42no—
357Q8×C107—42no—
358Q8×C107—42no—
359Q8×C107—42no—
360Q8×C107—42no—
361Q8×C107—42no—
362Q8×C107—41no—
363Q8×C107—41no—
364Q8×C107—41no—
365Q8×C107—41no—
366D4×C107—22no—
367D4×C107—22no—
368D4×C107—22no—
369D4×C107—22no—
370D4×C107—42no—
371D4×C107—42no—
372D4×C107—42no—
373D4×C107—42no—
374D4×C107—42no—
375D4×C107—42no—
376D4×C107—42no—
377D4×C107—42no—
378D4×C107—41no—
379D4×C107—41no—
380D4×C107—41no—
381D4×C107—41no—
382C2×C4×C107—24no—
383C2×C4×C107—24no—
384C2×C4×C107—22no—
385C2×C4×C107—22no—
386C2×C4×C107—44no—
387C2×C4×C107—42no—
388C2×C4×C107—42no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—42no—
392C2×C4×C107—42no—
393C2×C4×C107—42no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—42no—
397C2×C4×C107—42no—
398C2×C4×C107—42no—
399C2×C4×C107—42no—
400C2×C4×C107—42no—
401C2×C4×C107—42no—
402C2×C4×C107—42no—
403C2×C4×C107—42no—
404C2×C4×C107—42no—
405C2×C4×C107—42no—
406C2×C4×C107—82no—
407C2×C4×C107#12011yescharacteristic
408C2×C4×C107#12011yescharacteristic
409C2×C4×C107#12011yescharacteristic
410C2×C4×C107#12011yescharacteristic
411C2×C4×C107#12011yescharacteristic
412C2×C4×C107#12011yescharacteristic
413C2×C4×C107#12011yescharacteristic
414C2×C4×C107#12011yescharacteristic
415C2×C4×C107#12011yescharacteristic
416C2×C4×C107#12011yescharacteristic
417C2×C4×C107#12111yescharacteristic
418C2×C4×C107#12111yescharacteristic
419C2×C4×C107#12111yescharacteristic
420C2×C4×C107#12111yescharacteristic
421C2×C4×C107#12111yescharacteristic
422C2×C4×C107#12111yescharacteristic
423C2×C4×C107#12111yescharacteristic
424C2×C4×C107#12111yescharacteristic
425C2×C4×C107#12111yescharacteristic
426C2×C4×C107#12111yescharacteristic
427C2×C4×C107#12711yescharacteristic
428C2×C4×C107#12711yescharacteristic
429C2×C4×C107C22×D411yescharacteristic
430C2×C4×C107C22×D411yescharacteristic
431C2×C4×C107C22×D411yescharacteristic
432C2×C4×C107C22×D411yescharacteristic
433C2×C4×C107C22×D411yescharacteristic
434C2×C4×C107C2×#4111yescharacteristic
435C8×C107—24no—
436C8×C107—24no—
437C22×C107—22no—
438C22×C107—22no—
439C22×C107—22no—
440C22×C107—41no—
441C22×C107—41no—
442C22×C107—41no—
443C22×C107—41no—
444C22×C107—44no—
445C22×C107—42no—
446C22×C107—42no—
447C22×C107—82no—
448C22×C107—82no—
449C22×C107—82no—
450C22×C107—82no—
451C22×C107—82no—
452C22×C107#39211yescharacteristic
453C22×C107#39211yescharacteristic
454C22×C107#39211yescharacteristic
455C22×C107#39211yescharacteristic
456C22×C107C2×#12011yescharacteristic
457C22×C107C2×#12111yescharacteristic
458C22×C107C2×#12711yescharacteristic
459C4×C107—44no—
460C4×C107—42no—
461C4×C107—42no—
462C4×C107—44no—
463C4×C107—82no—
464C4×C107#39211yescharacteristic
465C4×C107#39211yescharacteristic
466C4×C107#39211yescharacteristic
467C4×C107#39211yescharacteristic
468C4×C107C2×#12011yescharacteristic
469C4×C107C2×#12011yescharacteristic
470C4×C107C2×#12111yescharacteristic
471C4×C107C2×#12111yescharacteristic
472C2×#2009C10711yesmaximal, characteristic, direct product factor, Sylow
473C2×C107—21no—
474C2×C107—21no—
475C2×C107—21no—
476C2×C107—21no—
477C2×C107—21no—
478C2×C107—21no—
479C2×C107—82no—
480C2×C107—82no—
481C2×C107#200912yesdirect product factor
482C2×C107C2×#39211yescharacteristic
483C2×#575C2×C10711yescharacteristic
484C22×#137C2×C10711yescharacteristic, complemented
485C2×#536C2×C10711yescharacteristic, complemented
486C2×#421C2×C10711yescharacteristic, complemented
487C2×#419C2×C10711yescharacteristic, complemented
488C2×#410C2×C10711yescharacteristic, complemented
489#2009C2×C10718yesdirect product factor
490C2×#344C2×C10711yescharacteristic, complemented
491C107C2×#200911yescharacteristic, direct product factor, Sylow
492C22×#41C22×C10711yescharacteristic
493C22×#41C22×C10711yescharacteristic
494C23×Q8C22×C10711yescharacteristic
495#575—22no—
496#575—22no—
497#575—22no—
498#575C22×C10714yes—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—22no—
502C2×#137—21no—
503C2×#137—21no—
504C2×#137—22no—
505C2×#137—22no—
506C2×#137C22×C10714yescomplemented
507C2×AGL(1,ℤ/8)—21no—
508C2×AGL(1,ℤ/8)—21no—
509C2×#135—22no—
510C22×Q16—21no—
511C22×SD16—21no—
512C22×M16C22×C10711yescharacteristic
513C22×M16C22×C10711yescharacteristic
514#536—22no—
515#536—22no—
516#536—22no—
517#536C22×C10714yescomplemented
518C2×C4⋊Q8—21no—
519C2×#124—21no—
520C2×#123—22no—
521C2×C22⋊Q8—22no—
522C2×#117C22×C10711yescharacteristic
523C2×#117C22×C10711yescharacteristic
524#421—22no—
525#421C22×C10714yescomplemented
526C2×#104—22no—
527#419—22no—
528#419C22×C10714yescomplemented
529C2×#103—22no—
530#410—22no—
531#410C22×C10714yescomplemented
532C2×#99—22no—
533#344C22×C10714yescomplemented
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41D4×C10712yes—
555C2×#41D4×C10712yes—
556C2×#41C23×C10712yes—
557C2×#41C23×C10712yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8D4×C10712yes—
570C22×Q8D4×C10711yescharacteristic
571C22×Q8D4×C10712yes—
572C22×Q8D4×C10711yescharacteristic
573C22×Q8C23×C10712yes—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4D4×C10711yescharacteristic
577C22×D4D4×C10711yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—21no—
581C23×C4C23×C10711yescharacteristic
582#137—28no—
583#137—28no—
584#137—24no—
585#137—24no—
586#137—28no—
587#137—24no—
588#137—24no—
589#137—28no—
590AGL(1,ℤ/8)—24no—
591AGL(1,ℤ/8)—24no—
592AGL(1,ℤ/8)—24no—
593AGL(1,ℤ/8)—24no—
594#135—28no—
595#135—28no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—22no—
599C2×Q16—24no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—24no—
605C2×D8—22no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16—21no—
611C2×M16—21no—
612C2×M16—21no—
613C2×M16D4×C10712yes—
614C2×M16D4×C10712yes—
615C2×M16D4×C10712yes—
616C2×M16C23×C10712yes—
617C2×M16C23×C10712yes—
618C22×C8—21no—
619C22×C8D4×C10712yes—
620C4⋊Q8—24no—
621C4⋊Q8—24no—
622#124—24no—
623#124—24no—
624#123—28no—
625#123—28no—
626C22⋊Q8—28no—
627C22⋊Q8—28no—
628#117—21no—
629#117—21no—
630#117—21no—
631#117—21no—
632#117—21no—
633#117D4×C10712yes—
634#117C23×C10712yes—
635#117C23×C10712yes—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C10712yes—
642C2×C42—21no—
643C2×C42—21no—
644#104—28no—
645#103—28no—
646#99—28no—
647C24—21no—
648C24—21no—
649C24C2×D4×C10711yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—22no—
659#41—22no—
660#41—22no—
661#41—22no—
662#41—22no—
663#41—22no—
664#41—22no—
665#41—22no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671#41—41no—
672#41—41no—
673#41—41no—
674#41—41no—
675#41—41no—
676#41—41no—
677#41—41no—
678#41—41no—
679#41—41no—
680#41—41no—
681#41—41no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—22no—
704C2×Q8—22no—
705C2×Q8—22no—
706C2×Q8—22no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—41no—
715C2×Q8—41no—
716C2×Q8—41no—
717C2×Q8—41no—
718C2×Q8—41no—
719C2×Q8C2×D4×C10714yes—
720C2×Q8C2×D4×C10712yes—
721C2×Q8C2×D4×C10712yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4C2×D4×C10712yes—
745C2×D4C2×D4×C10712yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—41no—
761C22×C4—41no—
762C22×C4—41no—
763C22×C4—41no—
764C22×C4—41no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—41no—
769C22×C4C2×D4×C10711yescharacteristic
770C22×C4C2×D4×C10711yescharacteristic
771C22×C4C2×D4×C10711yescharacteristic
772C22×C4C2×D4×C10711yescharacteristic
773C22×C4C2×D4×C10711yescharacteristic
774C22×C4C2×D4×C10711yescharacteristic
775C22×C4C2×D4×C10711yescharacteristic
776C22×C4C2×D4×C10711yescharacteristic
777C22×C4C2×D4×C10711yescharacteristic
778C22×C4C2×D4×C10711yescharacteristic
779C22×C4C2×D4×C10711yescharacteristic
780C22×C4#41×C10711yescharacteristic
781C22×C4#41×C10711yescharacteristic
782C22×C4C24×C10711yescharacteristic
783Q16—216no—
784Q16—28no—
785SD16—216no—
786SD16—28no—
787SD16—28no—
788D8—28no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—22no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16C2×D4×C10714yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8C2×D4×C10714yes—
803C4⋊C4—216no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—22no—
807C4⋊C4—41no—
808C22⋊C4—216no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—41no—
812C22⋊C4C2×D4×C10714yes—
813C42—22no—
814C42—22no—
815C42—22no—
816C42—41no—
817C23—22no—
818C23—22no—
819C23—42no—
820C23—44no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—82no—
826C23#120×C10711yescharacteristic
827C23#120×C10711yescharacteristic
828C23#121×C10711yescharacteristic
829C23#121×C10711yescharacteristic
830C23#127×C10711yescharacteristic
831C23#127×C10711yescharacteristic
832C23C22×D4×C10711yescharacteristic
833Q8—24no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—24no—
838Q8—22no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—41no—
847Q8—42no—
848Q8—42no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—22no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—42no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—44no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—82no—
890C2×C4#120×C10711yescharacteristic
891C2×C4#120×C10711yescharacteristic
892C2×C4#120×C10711yescharacteristic
893C2×C4#120×C10711yescharacteristic
894C2×C4#120×C10711yescharacteristic
895C2×C4#120×C10711yescharacteristic
896C2×C4#120×C10711yescharacteristic
897C2×C4#120×C10711yescharacteristic
898C2×C4#120×C10711yescharacteristic
899C2×C4#120×C10711yescharacteristic
900C2×C4#121×C10711yescharacteristic
901C2×C4#121×C10711yescharacteristic
902C2×C4#121×C10711yescharacteristic
903C2×C4#121×C10711yescharacteristic
904C2×C4#121×C10711yescharacteristic
905C2×C4#121×C10711yescharacteristic
906C2×C4#121×C10711yescharacteristic
907C2×C4#121×C10711yescharacteristic
908C2×C4#121×C10711yescharacteristic
909C2×C4#121×C10711yescharacteristic
910C2×C4#127×C10711yescharacteristic
911C2×C4#127×C10711yescharacteristic
912C2×C4C22×D4×C10711yescharacteristic
913C2×C4C22×D4×C10711yescharacteristic
914C2×C4C22×D4×C10711yescharacteristic
915C2×C4C22×D4×C10711yescharacteristic
916C2×C4C22×D4×C10711yescharacteristic
917C2×C4C2×#41×C10711yescharacteristic
918C8—24no—
919C8—24no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22#392×C10711yescharacteristic
936C22#392×C10711yescharacteristic
937C22#392×C10711yescharacteristic
938C22#392×C10711yescharacteristic
939C22C2×#120×C10711yescharacteristic
940C22C2×#121×C10711yescharacteristic
941C22C2×#127×C10711yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4#392×C10711yescharacteristic
948C4#392×C10711yescharacteristic
949C4#392×C10711yescharacteristic
950C4#392×C10711yescharacteristic
951C4C2×#120×C10711yescharacteristic
952C4C2×#120×C10711yescharacteristic
953C4C2×#121×C10711yescharacteristic
954C4C2×#121×C10711yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2C107×#200912yesdirect product factor
964C2C2×#392×C10711yescharacteristic
subgroupG/H
center, socleC22×C107#392
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#575×C107C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#137×C107C2semidirect
3. C2×#536×C107C2semidirect
4. C2×#421×C107C2semidirect
5. C2×#419×C107C2semidirect
6. C2×#410×C107C2semidirect
7. C107×#2009C2direct (N × H)
8. C2×#344×C107C2semidirect
23. C2×#137×C107C22semidirect
34. #536×C107C22semidirect
42. #421×C107C22semidirect
45. #419×C107C22semidirect
48. #410×C107C22semidirect
50. #344×C107C22semidirect
472. C2×#2009C107direct (N × H)
481. C2×C107#2009direct (N × H)
484. C22×#137C2×C107semidirect
485. C2×#536C2×C107semidirect
486. C2×#421C2×C107semidirect
487. C2×#419C2×C107semidirect
488. C2×#410C2×C107semidirect
489. #2009C2×C107direct (N × H)
490. C2×#344C2×C107semidirect
491. C107C2×#2009direct (N × H)
506. C2×#137C22×C107semidirect
517. #536C22×C107semidirect
525. #421C22×C107semidirect
528. #419C22×C107semidirect
531. #410C22×C107semidirect
533. #344C22×C107semidirect
963. C2C107×#2009direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#575×C1072
C22×#137×C1072
C2×#536×C1072
C2×#421×C1072
C2×#419×C1072
C2×#410×C1072
C107×#20092
C2×#344×C1072
C2×#2009107