Finite Group Databasebeta

← C107×#25508 #41051472

Subgroups — C107×#25508 #41051472

Order 27392.

1198 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C107C211yesmaximal, characteristic, complemented
2C2×#469×C107C211yesmaximal, characteristic, complemented
3C2×#466×C107C211yesmaximal, characteristic, complemented
4C107×#2624C211yesmaximal, characteristic, complemented
5C107×#2059C211yesmaximal, characteristic, complemented
6C107×#2041C211yesmaximal, characteristic, complemented
7C107×#2025C211yesmaximal, characteristic, complemented
8C107×#2011C211yesmaximal, characteristic, complemented
9C107×#1895C211yesmaximal, characteristic, complemented
10C107×#1893C211yesmaximal, characteristic, complemented
11C107×#1879C211yesmaximal, characteristic, complemented
12C107×#1879C211yesmaximal, characteristic, complemented
13C107×#1864C211yesmaximal, characteristic, complemented
14C107×#1862C211yesmaximal, characteristic, complemented
15C107×#1729C211yesmaximal, characteristic, complemented
16C22×D8×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×M16×C107C2211yescharacteristic
19C23×C8×C107C2211yescharacteristic
20#540×C107—24no—
21#540×C107—24no—
22C2×#127×C107C2211yescharacteristic
23C2×#125×C107C2211yescharacteristic
24C2×#123×C107—21no—
25C2×#123×C107—21no—
26C2×#121×C107—21no—
27C2×#121×C107—21no—
28C2×#121×C107C2211yescharacteristic
29C2×#121×C107C2211yescharacteristic
30C2×#121×C107C2211yescharacteristic
31C2×C4×D4×C107C2211yescharacteristic
32C2×C4×D4×C107C2211yescharacteristic
33C2×#117×C107C2211yescharacteristic
34#469×C107—24no—
35#466×C107—24no—
36C2×#107×C107C2211yescharacteristic
37C2×#106×C107C2211yescharacteristic
38C2×#102×C107C2211yescharacteristic
39C2×#102×C107C2211yescharacteristic
40C2×#102×C107C2211yescharacteristic
41C2×#102×C107C2211yescharacteristic
42C2×#102×C107C2211yescharacteristic
43C2×#102×C107C2211yescharacteristic
44C2×#102×C107C2211yescharacteristic
45C2×#102×C107C2211yescharacteristic
46#399×C107—21no—
47#397×C107—21no—
48#394×C107—21no—
49#394×C107—21no—
50#390×C107C2211yescharacteristic
51#390×C107C2211yescharacteristic
52#389×C107C2211yescharacteristic
53#389×C107C2211yescharacteristic
54#380×C107C2211yescharacteristic
55#340×C107C2211yescharacteristic
56#340×C107C2211yescharacteristic
57#340×C107C2211yescharacteristic
58#340×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61#336×C107C2211yescharacteristic
62#336×C107C2211yescharacteristic
63C22×D4×C107—21no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—21no—
67C22×D4×C107—21no—
68C22×D4×C107C2311yescharacteristic
69C22×D4×C107C2311yescharacteristic
70C22×D4×C107C2311yescharacteristic
71C23×C4×C107—21no—
72C23×C4×C107—21no—
73C23×C4×C107C2311yescharacteristic
74C2×D8×C107—22no—
75C2×D8×C107—22no—
76C2×D8×C107—22no—
77C2×D8×C107—22no—
78C2×D8×C107—41no—
79C2×D8×C107—41no—
80C2×M16×C107—22no—
81C2×M16×C107—22no—
82C2×M16×C107—41no—
83C22×C8×C107—22no—
84C22×C8×C107—22no—
85C22×C8×C107—41no—
86C22×C8×C107C2311yescharacteristic
87C22×C8×C107C2311yescharacteristic
88C22×C8×C107C2311yescharacteristic
89C22×C8×C107C2311yescharacteristic
90#127×C107—22no—
91#127×C107—22no—
92#125×C107—22no—
93#125×C107—22no—
94#123×C107—28no—
95#123×C107—28no—
96#121×C107—28no—
97#121×C107—28no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—22no—
101#121×C107—22no—
102#121×C107D414yes—
103#121×C107D414yes—
104C4×D4×C107—22no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108#117×C107—22no—
109#117×C107—22no—
110C2×C4⋊C4×C107—21no—
111C2×C4⋊C4×C107—21no—
112C2×C4⋊C4×C107—21no—
113C2×C4⋊C4×C107—21no—
114C2×C4⋊C4×C107D411yescharacteristic
115C2×C4⋊C4×C107D411yescharacteristic
116C2×C4⋊C4×C107C2311yescharacteristic
117C2×C4⋊C4×C107C2311yescharacteristic
118C2×C4⋊C4×C107C2311yescharacteristic
119C2×C4⋊C4×C107C2311yescharacteristic
120C2×C4⋊C4×C107C2311yescharacteristic
121C2×C22⋊C4×C107—21no—
122C2×C22⋊C4×C107—21no—
123C2×C22⋊C4×C107—21no—
124C2×C22⋊C4×C107—21no—
125C2×C22⋊C4×C107—21no—
126C2×C22⋊C4×C107—21no—
127C2×C22⋊C4×C107—21no—
128C2×C22⋊C4×C107—21no—
129C2×C22⋊C4×C107—21no—
130C2×C22⋊C4×C107—21no—
131C2×C22⋊C4×C107D411yescharacteristic
132C2×C22⋊C4×C107D411yescharacteristic
133C2×C42×C107C2311yescharacteristic
134C2×C42×C107C2311yescharacteristic
135#107×C107—22no—
136#106×C107—22no—
137#102×C107—22no—
138#102×C107—22no—
139#102×C107—22no—
140#102×C107—22no—
141#102×C107—22no—
142#102×C107—22no—
143#102×C107—41no—
144#102×C107—41no—
145#95×C107—21no—
146#95×C107—21no—
147#95×C107—21no—
148C24×C107—21no—
149C24×C107—21no—
150C24×C107—21no—
151C24×C107C2×D411yescharacteristic
152C2×D4×C107—24no—
153C2×D4×C107—24no—
154C2×D4×C107—24no—
155C2×D4×C107—24no—
156C2×D4×C107—21no—
157C2×D4×C107—21no—
158C2×D4×C107—21no—
159C2×D4×C107—21no—
160C2×D4×C107—21no—
161C2×D4×C107—21no—
162C2×D4×C107—21no—
163C2×D4×C107—21no—
164C2×D4×C107—21no—
165C2×D4×C107—21no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—21no—
169C2×D4×C107—21no—
170C2×D4×C107—21no—
171C2×D4×C107—21no—
172C2×D4×C107—42no—
173C2×D4×C107—81no—
174C2×D4×C107—81no—
175C2×D4×C107—81no—
176C2×D4×C107—81no—
177C2×D4×C107—81no—
178C2×D4×C107—81no—
179C2×D4×C107—81no—
180C2×D4×C107—81no—
181C2×D4×C107—81no—
182C2×D4×C107—81no—
183C2×D4×C107C2×D412yes—
184C2×D4×C107C2×D412yes—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—24no—
192C22×C4×C107—24no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
196C22×C4×C107—81no—
197C22×C4×C107—81no—
198C22×C4×C107—81no—
199C22×C4×C107—81no—
200C22×C4×C107C2×D411yescharacteristic
201C22×C4×C107C2×D411yescharacteristic
202C22×C4×C107C2×D411yescharacteristic
203C22×C4×C107C2×D411yescharacteristic
204C22×C4×C107C2×D411yescharacteristic
205C22×C4×C107C2×D412yes—
206C22×C4×C107C2×D412yes—
207C22×C4×C107C2411yescharacteristic
208D8×C107—44no—
209D8×C107—44no—
210M16×C107—44no—
211C2×C8×C107—21no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107—21no—
217C2×C8×C107—21no—
218C2×C8×C107—21no—
219C2×C8×C107—21no—
220C2×C8×C107—21no—
221C2×C8×C107—44no—
222C2×C8×C107#4112yes—
223C2×C8×C107#4112yes—
224C4⋊C4×C107—24no—
225C4⋊C4×C107—24no—
226C4⋊C4×C107—22no—
227C4⋊C4×C107—22no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—81no—
237C4⋊C4×C107—81no—
238C4⋊C4×C107C2×D412yes—
239C4⋊C4×C107C2×D412yes—
240C22⋊C4×C107—24no—
241C22⋊C4×C107—24no—
242C22⋊C4×C107—22no—
243C22⋊C4×C107—22no—
244C22⋊C4×C107—24no—
245C22⋊C4×C107—24no—
246C22⋊C4×C107—42no—
247C22⋊C4×C107—81no—
248C22⋊C4×C107—81no—
249C22⋊C4×C107—81no—
250C22⋊C4×C107—81no—
251C22⋊C4×C107—81no—
252C42×C107—21no—
253C42×C107—21no—
254C42×C107—21no—
255C42×C107—21no—
256C23×C107—21no—
257C23×C107—21no—
258C23×C107—21no—
259C23×C107—21no—
260C23×C107—21no—
261C23×C107—21no—
262C23×C107—22no—
263C23×C107—22no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—41no—
268C23×C107—41no—
269C23×C107—41no—
270C23×C107—41no—
271C23×C107—41no—
272C23×C107—41no—
273C23×C107—41no—
274C23×C107—41no—
275C23×C107—41no—
276C23×C107—41no—
277C23×C107—41no—
278C23×C107—41no—
279C23×C107—41no—
280C23×C107—41no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107#12012yes—
284C23×C107C22×D411yescharacteristic
285D4×C107—22no—
286D4×C107—22no—
287D4×C107—22no—
288D4×C107—22no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—41no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—41no—
297D4×C107—84no—
298D4×C107—84no—
299D4×C107—84no—
300D4×C107—84no—
301D4×C107—84no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—22no—
305C2×C4×C107—22no—
306C2×C4×C107—22no—
307C2×C4×C107—22no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—22no—
313C2×C4×C107—22no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—41no—
334C2×C4×C107—41no—
335C2×C4×C107—84no—
336C2×C4×C107—84no—
337C2×C4×C107#12012yes—
338C2×C4×C107C22×D411yescharacteristic
339C2×C4×C107C22×D411yescharacteristic
340C2×C4×C107C2×#4111yescharacteristic
341C2×C4×C107C2×#4111yescharacteristic
342C2×C4×C107H(5,𝔽2)11yescharacteristic
343C2×C4×C1072−1+411yescharacteristic
344C8×C107—22no—
345C8×C107—22no—
346C8×C107—41no—
347C8×C107—41no—
348C22×C107—22no—
349C22×C107—22no—
350C22×C107—22no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—42no—
356C22×C107—42no—
357C22×C107—42no—
358C22×C107—42no—
359C22×C107—42no—
360C22×C107—42no—
361C22×C107—81no—
362C22×C107—81no—
363C22×C107—81no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107—81no—
368C22×C107—81no—
369C22×C107—81no—
370C22×C107—81no—
371C22×C107—81no—
372C22×C107—81no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107C2×#12011yescharacteristic
377C22×C107#53211yescharacteristic
378C22×C107#53711yescharacteristic
379C22×C107#57611yescharacteristic
380C22×C107#57611yescharacteristic
381C22×C107#57611yescharacteristic
382C22×C107#57711yescharacteristic
383C4×C107—22no—
384C4×C107—41no—
385C4×C107—41no—
386C4×C107—42no—
387C4×C107—41no—
388C4×C107—41no—
389C4×C107—42no—
390C4×C107—81no—
391C4×C107—81no—
392C4×C107—81no—
393C4×C107#54611yescharacteristic
394C4×C107#54611yescharacteristic
395C4×C107#54711yescharacteristic
396C4×C107#54711yescharacteristic
397#25508C10711yesmaximal, characteristic, direct product factor, Sylow
398C2×C107—42no—
399C2×C107—82no—
400C2×C107—82no—
401C2×C107—161no—
402C2×C107#243011yescharacteristic
403C2×C107#300811yescharacteristic
404C2×C107#301211yescharacteristic
405C2×C107#317611yescharacteristic
406C2×C107#317911yescharacteristic
407C2×C107#325711yescharacteristic
408C2×C107#325911yescharacteristic
409C2×#540C2×C10711yescharacteristic, complemented
410C2×#469C2×C10711yescharacteristic, complemented
411C2×#466C2×C10711yescharacteristic, complemented
412#2624C2×C10711yescharacteristic, complemented
413#2059C2×C10711yescharacteristic, complemented
414#2041C2×C10711yescharacteristic, complemented
415#2025C2×C10711yescharacteristic, complemented
416#2011C2×C10711yescharacteristic, complemented
417#1895C2×C10711yescharacteristic, complemented
418#1893C2×C10711yescharacteristic, complemented
419#1879C2×C10711yescharacteristic, complemented
420#1879C2×C10711yescharacteristic, complemented
421#1864C2×C10711yescharacteristic, complemented
422#1862C2×C10711yescharacteristic, complemented
423#1729C2×C10711yescharacteristic, complemented
424C107#2550811yescharacteristic, direct product factor, Sylow
425C22×D8C22×C10711yescharacteristic
426C22×D8C22×C10711yescharacteristic
427C22×M16C22×C10711yescharacteristic
428C23×C8C22×C10711yescharacteristic
429#540—24no—
430#540—24no—
431C2×#127C22×C10711yescharacteristic
432C2×#125C22×C10711yescharacteristic
433C2×#123—21no—
434C2×#123—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C10711yescharacteristic
438C2×#121C22×C10711yescharacteristic
439C2×#121C22×C10711yescharacteristic
440C2×C4×D4C22×C10711yescharacteristic
441C2×C4×D4C22×C10711yescharacteristic
442C2×#117C22×C10711yescharacteristic
443#469—24no—
444#466—24no—
445C2×#107C22×C10711yescharacteristic
446C2×#106C22×C10711yescharacteristic
447C2×#102C22×C10711yescharacteristic
448C2×#102C22×C10711yescharacteristic
449C2×#102C22×C10711yescharacteristic
450C2×#102C22×C10711yescharacteristic
451C2×#102C22×C10711yescharacteristic
452C2×#102C22×C10711yescharacteristic
453C2×#102C22×C10711yescharacteristic
454C2×#102C22×C10711yescharacteristic
455#399—21no—
456#397—21no—
457#394—21no—
458#394—21no—
459#390C22×C10711yescharacteristic
460#390C22×C10711yescharacteristic
461#389C22×C10711yescharacteristic
462#389C22×C10711yescharacteristic
463#380C22×C10711yescharacteristic
464#340C22×C10711yescharacteristic
465#340C22×C10711yescharacteristic
466#340C22×C10711yescharacteristic
467#340C22×C10711yescharacteristic
468#336C22×C10711yescharacteristic
469#336C22×C10711yescharacteristic
470#336C22×C10711yescharacteristic
471#336C22×C10711yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C23×C10711yescharacteristic
478C22×D4C23×C10711yescharacteristic
479C22×D4C23×C10711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C10711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8—41no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C22×C8—22no—
493C22×C8—22no—
494C22×C8—41no—
495C22×C8C23×C10711yescharacteristic
496C22×C8C23×C10711yescharacteristic
497C22×C8C23×C10711yescharacteristic
498C22×C8C23×C10711yescharacteristic
499#127—22no—
500#127—22no—
501#125—22no—
502#125—22no—
503#123—28no—
504#123—28no—
505#121—28no—
506#121—28no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121D4×C10714yes—
512#121D4×C10714yes—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4D4×C10711yescharacteristic
524C2×C4⋊C4D4×C10711yescharacteristic
525C2×C4⋊C4C23×C10711yescharacteristic
526C2×C4⋊C4C23×C10711yescharacteristic
527C2×C4⋊C4C23×C10711yescharacteristic
528C2×C4⋊C4C23×C10711yescharacteristic
529C2×C4⋊C4C23×C10711yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C10711yescharacteristic
541C2×C22⋊C4D4×C10711yescharacteristic
542C2×C42C23×C10711yescharacteristic
543C2×C42C23×C10711yescharacteristic
544#107—22no—
545#106—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102—41no—
553#102—41no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C10711yescharacteristic
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C10712yes—
593C2×D4C2×D4×C10712yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C10711yescharacteristic
610C22×C4C2×D4×C10711yescharacteristic
611C22×C4C2×D4×C10711yescharacteristic
612C22×C4C2×D4×C10711yescharacteristic
613C22×C4C2×D4×C10711yescharacteristic
614C22×C4C2×D4×C10712yes—
615C22×C4C2×D4×C10712yes—
616C22×C4C24×C10711yescharacteristic
617D8—44no—
618D8—44no—
619M16—44no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—44no—
631C2×C8#41×C10712yes—
632C2×C8#41×C10712yes—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—81no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C10712yes—
648C4⋊C4C2×D4×C10712yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23#120×C10712yes—
693C23C22×D4×C10711yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4#120×C10712yes—
747C2×C4C22×D4×C10711yescharacteristic
748C2×C4C22×D4×C10711yescharacteristic
749C2×C4C2×#41×C10711yescharacteristic
750C2×C4C2×#41×C10711yescharacteristic
751C2×C4H(5,𝔽2)×C10711yescharacteristic
752C2×C42−1+4×C10711yescharacteristic
753C8—22no—
754C8—22no—
755C8—41no—
756C8—41no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#120×C10711yescharacteristic
786C22#532×C10711yescharacteristic
787C22#537×C10711yescharacteristic
788C22#576×C10711yescharacteristic
789C22#576×C10711yescharacteristic
790C22#576×C10711yescharacteristic
791C22#577×C10711yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—42no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C10711yescharacteristic
803C4#546×C10711yescharacteristic
804C4#547×C10711yescharacteristic
805C4#547×C10711yescharacteristic
806C2—42no—
807C2—82no—
808C2—82no—
809C2—161no—
810C2C107×#243011yescharacteristic
811C2C107×#300811yescharacteristic
812C2C107×#301211yescharacteristic
813C2C107×#317611yescharacteristic
814C2C107×#317911yescharacteristic
815C2C107×#325711yescharacteristic
816C2C107×#325911yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×#117×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C107C2semidirect
2. C2×#469×C107C2semidirect
3. C2×#466×C107C2semidirect
4. C107×#2624C2semidirect
5. C107×#2059C2semidirect
6. C107×#2041C2semidirect
7. C107×#2025C2semidirect
8. C107×#2011C2semidirect
9. C107×#1895C2semidirect
10. C107×#1893C2semidirect
11. C107×#1879C2semidirect
12. C107×#1879C2semidirect
13. C107×#1864C2semidirect
14. C107×#1862C2semidirect
15. C107×#1729C2semidirect
397. #25508C107direct (N × H)
409. C2×#540C2×C107semidirect
410. C2×#469C2×C107semidirect
411. C2×#466C2×C107semidirect
412. #2624C2×C107semidirect
413. #2059C2×C107semidirect
414. #2041C2×C107semidirect
415. #2025C2×C107semidirect
416. #2011C2×C107semidirect
417. #1895C2×C107semidirect
418. #1893C2×C107semidirect
419. #1879C2×C107semidirect
420. #1879C2×C107semidirect
421. #1864C2×C107semidirect
422. #1862C2×C107semidirect
423. #1729C2×C107semidirect
424. C107#25508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#540×C1072
C2×#469×C1072
C2×#466×C1072
C107×#26242
C107×#20592
C107×#20412
C107×#20252
C107×#20112
C107×#18952
C107×#18932
C107×#18792
C107×#18642
C107×#18622
C107×#17292
#25508107