Finite Group Databasebeta

← C107×#23012 #41048976

Subgroups — C107×#23012 #41048976

Order 27392.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C107C211yesmaximal, characteristic
2C2×#440×C107C211yesmaximal, characteristic
3C2×C4×SD16×C107C211yesmaximal, characteristic
4C107×#2365C211yesmaximal, characteristic, complemented
5C107×#2349C211yesmaximal, characteristic
6C107×#1960C211yesmaximal, characteristic, complemented
7C107×#1949C211yesmaximal, characteristic, complemented
8C107×#1935C211yesmaximal, characteristic, complemented
9C107×#1933C211yesmaximal, characteristic, complemented
10C107×#1877C211yesmaximal, characteristic
11C107×#1877C211yesmaximal, characteristic
12C107×#1865C211yesmaximal, characteristic, complemented
13C107×#1863C211yesmaximal, characteristic, complemented
14C107×#1771C211yesmaximal, characteristic, complemented
15C107×#1762C211yesmaximal, characteristic
16C22×SD16×C107C2211yescharacteristic
17C22×SD16×C107C2211yescharacteristic
18C2×C4⋊Q8×C107C2211yescharacteristic
19C2×C4×Q8×C107C2211yescharacteristic
20C2×C4×Q8×C107C2211yescharacteristic
21C2×C4×D4×C107C2211yescharacteristic
22C2×C4×D4×C107C2211yescharacteristic
23C2×C4×D4×C107C2211yescharacteristic
24#461×C107C418yescomplemented
25#440×C107—24no—
26C4×SD16×C107—24no—
27C2×#107×C107C2211yescharacteristic
28C2×#106×C107C2211yescharacteristic
29C2×C4⋊C8×C107C2211yescharacteristic
30C2×#103×C107C2211yescharacteristic
31C2×#103×C107C2211yescharacteristic
32C2×#103×C107C2211yescharacteristic
33C2×#103×C107C2211yescharacteristic
34C2×#103×C107C2211yescharacteristic
35C2×#103×C107C2211yescharacteristic
36C2×#102×C107C2211yescharacteristic
37C2×#102×C107C2211yescharacteristic
38C2×#97×C107C2211yescharacteristic
39C2×#97×C107C2211yescharacteristic
40C2×C4×C8×C107C2211yescharacteristic
41#391×C107C2211yescharacteristic
42#391×C107C2211yescharacteristic
43#389×C107—21no—
44#389×C107C2211yescharacteristic
45#389×C107C2211yescharacteristic
46#387×C107—21no—
47#387×C107—21no—
48#385×C107—21no—
49#385×C107—21no—
50#382×C107C2211yescharacteristic
51#380×C107—21no—
52C4×C4⋊C4×C107—21no—
53C4×C4⋊C4×C107C2211yescharacteristic
54C4×C4⋊C4×C107C2211yescharacteristic
55C2×#95×C107—21no—
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#340×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62C22×Q8×C107C2311yescharacteristic
63C22×Q8×C107C2311yescharacteristic
64C22×D4×C107C2311yescharacteristic
65C23×C4×C107—21no—
66C23×C4×C107—21no—
67C23×C4×C107—21no—
68C2×SD16×C107—22no—
69C2×SD16×C107—22no—
70C2×SD16×C107—22no—
71C2×SD16×C107—22no—
72C2×SD16×C107C2×C414yes—
73C2×SD16×C107C2×C414yes—
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C4⋊Q8×C107—22no—
79C4⋊Q8×C107C2×C414yescomplemented
80C4×Q8×C107—22no—
81C4×Q8×C107—22no—
82C4×Q8×C107—41no—
83C4×Q8×C107—41no—
84C4×D4×C107—22no—
85C4×D4×C107—22no—
86C4×D4×C107—22no—
87C4×D4×C107—41no—
88C4×D4×C107—41no—
89C4×D4×C107C2×C414yes—
90C2×C4⋊C4×C107—21no—
91C2×C4⋊C4×C107—21no—
92C2×C4⋊C4×C107—21no—
93C2×C4⋊C4×C107—21no—
94C2×C4⋊C4×C107—21no—
95C2×C4⋊C4×C107—21no—
96C2×C4⋊C4×C107D411yescharacteristic
97C2×C4⋊C4×C107D411yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C4⋊C4×C107C2311yescharacteristic
100C2×C4⋊C4×C107C2311yescharacteristic
101C2×C4⋊C4×C107C2311yescharacteristic
102C2×C4⋊C4×C107C2311yescharacteristic
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C42×C107—21no—
107C2×C42×C107—21no—
108C2×C42×C107—21no—
109C2×C42×C107C2311yescharacteristic
110C2×C42×C107C2311yescharacteristic
111C2×C42×C107C2311yescharacteristic
112#107×C107—22no—
113#106×C107—22no—
114C4⋊C8×C107C2×C414yescomplemented
115#103×C107—22no—
116#103×C107—22no—
117#103×C107—41no—
118#103×C107—41no—
119#103×C107C2×C414yescomplemented
120#103×C107C2×C414yescomplemented
121#102×C107—22no—
122#102×C107D414yes—
123#97×C107—22no—
124#97×C107—22no—
125C4×C8×C107—22no—
126#95×C107—21no—
127#95×C107—21no—
128#95×C107—21no—
129#95×C107—21no—
130#95×C107—21no—
131#95×C107—21no—
132#95×C107—21no—
133#95×C107—21no—
134#95×C107—21no—
135#95×C107D411yescharacteristic
136#95×C107D411yescharacteristic
137C24×C107—21no—
138C2×Q8×C107—21no—
139C2×Q8×C107—21no—
140C2×Q8×C107—21no—
141C2×Q8×C107—21no—
142C2×Q8×C107—21no—
143C2×Q8×C107—21no—
144C2×Q8×C107—21no—
145C2×Q8×C107—21no—
146C2×Q8×C107—21no—
147C2×Q8×C107—21no—
148C2×Q8×C107C22×C412yes—
149C2×Q8×C107C22×C412yes—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107C22×C412yes—
154C2×D4×C107C2×D412yes—
155C2×D4×C107#4112yes—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—24no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—42no—
165C22×C4×C107—42no—
166C22×C4×C107—42no—
167C22×C4×C107—42no—
168C22×C4×C107—81no—
169C22×C4×C107—81no—
170C22×C4×C107—81no—
171C22×C4×C107—81no—
172C22×C4×C107C2×D411yescharacteristic
173C22×C4×C107C2×D411yescharacteristic
174C22×C4×C107C2×D411yescharacteristic
175C22×C4×C107C2×D411yescharacteristic
176C22×C4×C107C2×D411yescharacteristic
177C22×C4×C107C2×D411yescharacteristic
178C22×C4×C107C2411yescharacteristic
179SD16×C107—28no—
180SD16×C107—28no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107—21no—
190C2×C8×C107C22×C412yes—
191C2×C8×C107C22×C412yes—
192C2×C8×C107C2×D412yes—
193C4⋊C4×C107—24no—
194C4⋊C4×C107—24no—
195C4⋊C4×C107—22no—
196C4⋊C4×C107—21no—
197C4⋊C4×C107—21no—
198C4⋊C4×C107—21no—
199C4⋊C4×C107—21no—
200C4⋊C4×C107—21no—
201C4⋊C4×C107—21no—
202C4⋊C4×C107—21no—
203C4⋊C4×C107—21no—
204C4⋊C4×C107—41no—
205C4⋊C4×C107—42no—
206C4⋊C4×C107—42no—
207C4⋊C4×C107—81no—
208C4⋊C4×C107—81no—
209C4⋊C4×C107C22×C412yes—
210C4⋊C4×C107C2×D412yes—
211C22⋊C4×C107—24no—
212C22⋊C4×C107—42no—
213C22⋊C4×C107—42no—
214C42×C107—21no—
215C42×C107—21no—
216C42×C107—21no—
217C42×C107—21no—
218C42×C107—42no—
219C42×C107—42no—
220C42×C107—42no—
221C42×C107C22×C412yes—
222C42×C107#4112yes—
223C23×C107—22no—
224C23×C107—22no—
225C23×C107—22no—
226C23×C107—41no—
227C23×C107—41no—
228C23×C107—41no—
229C23×C107—41no—
230C23×C107C22×D411yescharacteristic
231Q8×C107—22no—
232Q8×C107—22no—
233Q8×C107—22no—
234Q8×C107—22no—
235Q8×C107—41no—
236Q8×C107—41no—
237Q8×C107—41no—
238Q8×C107—41no—
239D4×C107—22no—
240D4×C107—22no—
241D4×C107—22no—
242D4×C107C4×D414yes—
243C2×C4×C107—21no—
244C2×C4×C107—21no—
245C2×C4×C107—21no—
246C2×C4×C107—21no—
247C2×C4×C107—21no—
248C2×C4×C107—21no—
249C2×C4×C107—22no—
250C2×C4×C107—22no—
251C2×C4×C107—22no—
252C2×C4×C107—21no—
253C2×C4×C107—21no—
254C2×C4×C107—21no—
255C2×C4×C107—22no—
256C2×C4×C107—21no—
257C2×C4×C107—21no—
258C2×C4×C107—21no—
259C2×C4×C107—21no—
260C2×C4×C107—21no—
261C2×C4×C107—21no—
262C2×C4×C107—41no—
263C2×C4×C107—41no—
264C2×C4×C107—41no—
265C2×C4×C107—41no—
266C2×C4×C107—41no—
267C2×C4×C107—41no—
268C2×C4×C107—41no—
269C2×C4×C107—41no—
270C2×C4×C107—41no—
271C2×C4×C107—41no—
272C2×C4×C107—41no—
273C2×C4×C107—41no—
274C2×C4×C107—41no—
275C2×C4×C107—41no—
276C2×C4×C107—41no—
277C2×C4×C107—41no—
278C2×C4×C107—41no—
279C2×C4×C107—84no—
280C2×C4×C107—84no—
281C2×C4×C107—84no—
282C2×C4×C107C4×D412yes—
283C2×C4×C107C4×D412yes—
284C2×C4×C107#13712yes—
285C2×C4×C107C23×C411yescharacteristic
286C2×C4×C107C22×D411yescharacteristic
287C2×C4×C107C2×#4111yescharacteristic
288C2×C4×C107C2×#4111yescharacteristic
289C2×C4×C107H(5,𝔽2)11yescharacteristic
290C2×C4×C1072−1+411yescharacteristic
291C8×C107—22no—
292C8×C107—22no—
293C8×C107—22no—
294C8×C107—41no—
295C22×C107—24no—
296C22×C107—42no—
297C22×C107—42no—
298C22×C107—42no—
299C22×C107—42no—
300C22×C107—42no—
301C22×C107—42no—
302C22×C107C2×C4×D411yescharacteristic
303C22×C107D4211yescharacteristic
304C22×C107#54811yescharacteristic
305C22×C107C2×#13711yescharacteristic
306C22×C107#57511yescharacteristic
307C22×C107#57711yescharacteristic
308C22×C107#57711yescharacteristic
309C4×C107—22no—
310C4×C107—22no—
311C4×C107—22no—
312C4×C107—42no—
313C4×C107—42no—
314C4×C107—42no—
315C4×C107—41no—
316C4×C107—41no—
317C4×C107—41no—
318C4×C107—42no—
319C4×C107—81no—
320C4×C107—81no—
321C4×C107—81no—
322C4×C107C2×C4×D411yescharacteristic
323C4×C107#52011yescharacteristic
324C4×C107#54711yescharacteristic
325C4×C107#55311yescharacteristic
326#23012C10711yesmaximal, characteristic, direct product factor, Sylow
327C2×C107—44no—
328C2×C107#236111yescharacteristic
329C2×C107C4×#13711yescharacteristic
330C2×C107#294911yescharacteristic
331C2×C107#326611yescharacteristic
332C2×C107#326711yescharacteristic
333C2×C107#337211yescharacteristic
334C2×C107#337611yescharacteristic
335C2×#461C2×C10711yescharacteristic
336C2×#440C2×C10711yescharacteristic
337C2×C4×SD16C2×C10711yescharacteristic
338#2365C2×C10711yescharacteristic, complemented
339#2349C2×C10711yescharacteristic
340#1960C2×C10711yescharacteristic, complemented
341#1949C2×C10711yescharacteristic, complemented
342#1935C2×C10711yescharacteristic, complemented
343#1933C2×C10711yescharacteristic, complemented
344#1877C2×C10711yescharacteristic
345#1877C2×C10711yescharacteristic
346#1865C2×C10711yescharacteristic, complemented
347#1863C2×C10711yescharacteristic, complemented
348#1771C2×C10711yescharacteristic, complemented
349#1762C2×C10711yescharacteristic
350C107#2301211yescharacteristic, direct product factor, Sylow
351C22×SD16C22×C10711yescharacteristic
352C22×SD16C22×C10711yescharacteristic
353C2×C4⋊Q8C22×C10711yescharacteristic
354C2×C4×Q8C22×C10711yescharacteristic
355C2×C4×Q8C22×C10711yescharacteristic
356C2×C4×D4C22×C10711yescharacteristic
357C2×C4×D4C22×C10711yescharacteristic
358C2×C4×D4C22×C10711yescharacteristic
359#461C4×C10718yescomplemented
360#440—24no—
361C4×SD16—24no—
362C2×#107C22×C10711yescharacteristic
363C2×#106C22×C10711yescharacteristic
364C2×C4⋊C8C22×C10711yescharacteristic
365C2×#103C22×C10711yescharacteristic
366C2×#103C22×C10711yescharacteristic
367C2×#103C22×C10711yescharacteristic
368C2×#103C22×C10711yescharacteristic
369C2×#103C22×C10711yescharacteristic
370C2×#103C22×C10711yescharacteristic
371C2×#102C22×C10711yescharacteristic
372C2×#102C22×C10711yescharacteristic
373C2×#97C22×C10711yescharacteristic
374C2×#97C22×C10711yescharacteristic
375C2×C4×C8C22×C10711yescharacteristic
376#391C22×C10711yescharacteristic
377#391C22×C10711yescharacteristic
378#389—21no—
379#389C22×C10711yescharacteristic
380#389C22×C10711yescharacteristic
381#387—21no—
382#387—21no—
383#385—21no—
384#385—21no—
385#382C22×C10711yescharacteristic
386#380—21no—
387C4×C4⋊C4—21no—
388C4×C4⋊C4C22×C10711yescharacteristic
389C4×C4⋊C4C22×C10711yescharacteristic
390C2×#95—21no—
391#340C22×C10711yescharacteristic
392#340C22×C10711yescharacteristic
393#340C22×C10711yescharacteristic
394#340C22×C10711yescharacteristic
395#336C22×C10711yescharacteristic
396#336C22×C10711yescharacteristic
397C22×Q8C23×C10711yescharacteristic
398C22×Q8C23×C10711yescharacteristic
399C22×D4C23×C10711yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—21no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16—22no—
407C2×SD16C2×C4×C10714yes—
408C2×SD16C2×C4×C10714yes—
409C22×C8C23×C10711yescharacteristic
410C22×C8C23×C10711yescharacteristic
411C22×C8C23×C10711yescharacteristic
412C22×C8C23×C10711yescharacteristic
413C4⋊Q8—22no—
414C4⋊Q8C2×C4×C10714yescomplemented
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×Q8—41no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—41no—
423C4×D4—41no—
424C4×D4C2×C4×C10714yes—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C10711yescharacteristic
432C2×C4⋊C4D4×C10711yescharacteristic
433C2×C4⋊C4C23×C10711yescharacteristic
434C2×C4⋊C4C23×C10711yescharacteristic
435C2×C4⋊C4C23×C10711yescharacteristic
436C2×C4⋊C4C23×C10711yescharacteristic
437C2×C4⋊C4C23×C10711yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C10711yescharacteristic
445C2×C42C23×C10711yescharacteristic
446C2×C42C23×C10711yescharacteristic
447#107—22no—
448#106—22no—
449C4⋊C8C2×C4×C10714yescomplemented
450#103—22no—
451#103—22no—
452#103—41no—
453#103—41no—
454#103C2×C4×C10714yescomplemented
455#103C2×C4×C10714yescomplemented
456#102—22no—
457#102D4×C10714yes—
458#97—22no—
459#97—22no—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95D4×C10711yescharacteristic
471#95D4×C10711yescharacteristic
472C24—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8C22×C4×C10712yes—
484C2×Q8C22×C4×C10712yes—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C22×C4×C10712yes—
489C2×D4C2×D4×C10712yes—
490C2×D4#41×C10712yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4C2×D4×C10711yescharacteristic
508C22×C4C2×D4×C10711yescharacteristic
509C22×C4C2×D4×C10711yescharacteristic
510C22×C4C2×D4×C10711yescharacteristic
511C22×C4C2×D4×C10711yescharacteristic
512C22×C4C2×D4×C10711yescharacteristic
513C22×C4C24×C10711yescharacteristic
514SD16—28no—
515SD16—28no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8C22×C4×C10712yes—
526C2×C8C22×C4×C10712yes—
527C2×C8C2×D4×C10712yes—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—41no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4C22×C4×C10712yes—
545C4⋊C4C2×D4×C10712yes—
546C22⋊C4—24no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C42—42no—
556C42C22×C4×C10712yes—
557C42#41×C10712yes—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C22×D4×C10711yescharacteristic
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4C4×D4×C10714yes—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4—84no—
617C2×C4C4×D4×C10712yes—
618C2×C4C4×D4×C10712yes—
619C2×C4#137×C10712yes—
620C2×C4C23×C4×C10711yescharacteristic
621C2×C4C22×D4×C10711yescharacteristic
622C2×C4C2×#41×C10711yescharacteristic
623C2×C4C2×#41×C10711yescharacteristic
624C2×C4H(5,𝔽2)×C10711yescharacteristic
625C2×C42−1+4×C10711yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—41no—
630C22—24no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22C2×C4×D4×C10711yescharacteristic
638C22D42×C10711yescharacteristic
639C22#548×C10711yescharacteristic
640C22C2×#137×C10711yescharacteristic
641C22#575×C10711yescharacteristic
642C22#577×C10711yescharacteristic
643C22#577×C10711yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4C2×C4×D4×C10711yescharacteristic
658C4#520×C10711yescharacteristic
659C4#547×C10711yescharacteristic
660C4#553×C10711yescharacteristic
661C2—44no—
662C2C107×#236111yescharacteristic
663C2C4×#137×C10711yescharacteristic
664C2C107×#294911yescharacteristic
665C2C107×#326611yescharacteristic
666C2C107×#326711yescharacteristic
667C2C107×#337211yescharacteristic
668C2C107×#337611yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutatorC2×C4C23×C4×C107
Frattini, cosocleC22×C4C24×C107
prime radicalC22×D4×C107C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C4×C4⋊C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C107×#2365C2semidirect
6. C107×#1960C2semidirect
7. C107×#1949C2semidirect
8. C107×#1935C2semidirect
9. C107×#1933C2semidirect
12. C107×#1865C2semidirect
13. C107×#1863C2semidirect
14. C107×#1771C2semidirect
24. #461×C107C4semidirect
79. C4⋊Q8×C107C2×C4semidirect
114. C4⋊C8×C107C2×C4semidirect
119. #103×C107C2×C4semidirect
120. #103×C107C2×C4semidirect
326. #23012C107direct (N × H)
338. #2365C2×C107semidirect
340. #1960C2×C107semidirect
341. #1949C2×C107semidirect
342. #1935C2×C107semidirect
343. #1933C2×C107semidirect
346. #1865C2×C107semidirect
347. #1863C2×C107semidirect
348. #1771C2×C107semidirect
350. C107#23012direct (N × H)
359. #461C4×C107semidirect
414. C4⋊Q8C2×C4×C107semidirect
449. C4⋊C8C2×C4×C107semidirect
454. #103C2×C4×C107semidirect
455. #103C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1072
C2×#440×C1072
C2×C4×SD16×C1072
C107×#23652
C107×#23492
C107×#19602
C107×#19492
C107×#19352
C107×#19332
C107×#18772
C107×#18652
C107×#18632
C107×#17712
C107×#17622
#23012107