Finite Group Databasebeta

← C107×#24512 #41050476

Subgroups — C107×#24512 #41050476

Order 27392.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C107C211yesmaximal, characteristic
2C2×#433×C107C211yesmaximal, characteristic, complemented
3C107×#2624C211yesmaximal, characteristic, complemented
4C107×#2309C211yesmaximal, characteristic, complemented
5C107×#2067C211yesmaximal, characteristic, complemented
6C107×#2065C211yesmaximal, characteristic, complemented
7C107×#2054C211yesmaximal, characteristic, complemented
8C107×#2054C211yesmaximal, characteristic, complemented
9C107×#1972C211yesmaximal, characteristic, complemented
10C107×#1970C211yesmaximal, characteristic, complemented
11C107×#1936C211yesmaximal, characteristic, complemented
12C107×#1934C211yesmaximal, characteristic, complemented
13C107×#1875C211yesmaximal, characteristic, complemented
14C107×#1854C211yesmaximal, characteristic, complemented
15C107×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C107C2211yescharacteristic
17C22×D8×C107C2211yescharacteristic
18C22×D8×C107C2211yescharacteristic
19C2×#121×C107C2211yescharacteristic
20C2×#117×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22#447×C107—24no—
23#433×C107—24no—
24C2×#107×C107C2211yescharacteristic, complemented
25C2×#106×C107C2211yescharacteristic, complemented
26C2×C4⋊C8×C107C2211yescharacteristic, complemented
27C2×C4⋊C8×C107C2211yescharacteristic, complemented
28C2×#102×C107C2211yescharacteristic
29C2×#102×C107C2211yescharacteristic
30C2×#102×C107C2211yescharacteristic
31C2×#102×C107C2211yescharacteristic
32C2×#102×C107C2211yescharacteristic
33C2×#102×C107C2211yescharacteristic
34C2×#102×C107C2211yescharacteristic, complemented
35C2×#102×C107C2211yescharacteristic, complemented
36C2×C22⋊C8×C107C2211yescharacteristic
37C2×C22⋊C8×C107C2211yescharacteristic
38C2×#97×C107C2211yescharacteristic, complemented
39C2×C4×C8×C107C2211yescharacteristic, complemented
40#399×C107—21no—
41#397×C107—21no—
42#394×C107—21no—
43#394×C107—21no—
44#390×C107—21no—
45#390×C107—21no—
46#390×C107C2211yescharacteristic
47#390×C107C2211yescharacteristic
48#390×C107C2211yescharacteristic
49#390×C107C2211yescharacteristic
50#390×C107C2211yescharacteristic, complemented
51#390×C107C2211yescharacteristic, complemented
52#389×C107C2211yescharacteristic, complemented
53#389×C107C2211yescharacteristic, complemented
54#380×C107C2211yescharacteristic
55#379×C107—21no—
56#379×C107—21no—
57#340×C107C2211yescharacteristic, complemented
58#340×C107C2211yescharacteristic, complemented
59#340×C107C2211yescharacteristic, complemented
60#340×C107C2211yescharacteristic, complemented
61C25×C107—21no—
62C22×D4×C107—22no—
63C22×D4×C107—22no—
64C22×D4×C107—21no—
65C22×D4×C107—21no—
66C22×D4×C107—22no—
67C22×D4×C107—22no—
68C22×D4×C107—41no—
69C22×D4×C107—41no—
70C22×D4×C107C2311yescharacteristic
71C22×D4×C107C2311yescharacteristic
72C22×D4×C107C2311yescharacteristic
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—
80C22×C8×C107C2311yescharacteristic
81C22×C8×C107C2311yescharacteristic
82C22×C8×C107C2311yescharacteristic
83C22×C8×C107C2311yescharacteristic
84#121×C107—22no—
85#121×C107—22no—
86#117×C107—22no—
87#117×C107—22no—
88#117×C107—41no—
89#117×C107—41no—
90C2×C4⋊C4×C107—21no—
91C2×C4⋊C4×C107—21no—
92C2×C4⋊C4×C107D411yescharacteristic
93C2×C4⋊C4×C107D411yescharacteristic
94C2×C4⋊C4×C107C2311yescharacteristic
95C2×C4⋊C4×C107C2311yescharacteristic
96C2×C4⋊C4×C107C2311yescharacteristic
97C2×C4⋊C4×C107C2311yescharacteristic
98C2×C4⋊C4×C107C2311yescharacteristic
99C2×C22⋊C4×C107—21no—
100C2×C22⋊C4×C107—21no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—21no—
105C2×C22⋊C4×C107—21no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—21no—
108C2×C22⋊C4×C107—21no—
109C2×C22⋊C4×C107—21no—
110C2×C22⋊C4×C107—21no—
111C2×C22⋊C4×C107—21no—
112C2×C22⋊C4×C107—21no—
113C2×C22⋊C4×C107—21no—
114C2×C22⋊C4×C107D411yescharacteristic
115C2×C22⋊C4×C107D411yescharacteristic
116C2×C42×C107—21no—
117C2×C42×C107C2311yescharacteristic
118C2×C42×C107C2311yescharacteristic
119#107×C107—41no—
120#106×C107—41no—
121C4⋊C8×C107—22no—
122C4⋊C8×C107—22no—
123#102×C107—22no—
124#102×C107—22no—
125#102×C107—22no—
126#102×C107—22no—
127#102×C107—41no—
128#102×C107—41no—
129#102×C107—41no—
130#102×C107—41no—
131C22⋊C8×C107—22no—
132C22⋊C8×C107D414yes—
133#97×C107—22no—
134C4×C8×C107—22no—
135#95×C107—21no—
136#95×C107—21no—
137#95×C107—21no—
138C24×C107—24no—
139C24×C107—21no—
140C24×C107—21no—
141C24×C107—21no—
142C24×C107—42no—
143C24×C107—42no—
144C24×C107—81no—
145C24×C107—81no—
146C24×C107—81no—
147C24×C107—81no—
148C24×C107C2×D411yescharacteristic
149C2×D4×C107—24no—
150C2×D4×C107—21no—
151C2×D4×C107—21no—
152C2×D4×C107—21no—
153C2×D4×C107—21no—
154C2×D4×C107—21no—
155C2×D4×C107—21no—
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—44no—
167C2×D4×C107—44no—
168C2×D4×C107—44no—
169C2×D4×C107—44no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—42no—
173C2×D4×C107—81no—
174C2×D4×C107—81no—
175C2×D4×C107#4112yes—
176C2×D4×C107#4112yes—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107C2×D411yescharacteristic
187C22×C4×C107C2×D411yescharacteristic
188C22×C4×C107C2×D411yescharacteristic
189C22×C4×C107C2×D411yescharacteristic
190C22×C4×C107C2×D411yescharacteristic
191C22×C4×C107C2×D412yes—
192C22×C4×C107#4112yes—
193C22×C4×C107C2411yescharacteristic
194D8×C107—44no—
195D8×C107—44no—
196C2×C8×C107—21no—
197C2×C8×C107—21no—
198C2×C8×C107—21no—
199C2×C8×C107—21no—
200C2×C8×C107—21no—
201C2×C8×C107—21no—
202C2×C8×C107—21no—
203C2×C8×C107—21no—
204C2×C8×C107—21no—
205C2×C8×C107—21no—
206C2×C8×C107C2×D412yes—
207C2×C8×C107C2×D412yes—
208C4⋊C4×C107—22no—
209C4⋊C4×C107—22no—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—21no—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—81no—
221C4⋊C4×C107—81no—
222C22⋊C4×C107—22no—
223C22⋊C4×C107—22no—
224C22⋊C4×C107—42no—
225C22⋊C4×C107—42no—
226C22⋊C4×C107—81no—
227C22⋊C4×C107—81no—
228C22⋊C4×C107—81no—
229C22⋊C4×C107—81no—
230C22⋊C4×C107—81no—
231C22⋊C4×C107—81no—
232C22⋊C4×C107—81no—
233C22⋊C4×C107—81no—
234C22⋊C4×C107—81no—
235C22⋊C4×C107—81no—
236C22⋊C4×C107—81no—
237C22⋊C4×C107—81no—
238C22⋊C4×C107—81no—
239C42×C107—21no—
240C42×C107—21no—
241C42×C107—21no—
242C42×C107—21no—
243C42×C107—42no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—22no—
251C23×C107—22no—
252C23×C107—48no—
253C23×C107—41no—
254C23×C107—41no—
255C23×C107—41no—
256C23×C107—41no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—41no—
263C23×C107—41no—
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—84no—
273C23×C107—84no—
274C23×C107—84no—
275C23×C107—84no—
276C23×C107—84no—
277C23×C107—84no—
278C23×C107#12112yes—
279C23×C107C22×D411yescharacteristic
280D4×C107—22no—
281D4×C107—22no—
282D4×C107—22no—
283D4×C107—22no—
284D4×C107—48no—
285D4×C107—41no—
286D4×C107—41no—
287D4×C107—41no—
288D4×C107—41no—
289D4×C107—41no—
290D4×C107—41no—
291D4×C107—41no—
292D4×C107—41no—
293D4×C107—84no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—22no—
297C2×C4×C107—22no—
298C2×C4×C107—22no—
299C2×C4×C107—22no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—41no—
317C2×C4×C107—41no—
318C2×C4×C107—41no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107#12112yes—
328C2×C4×C107C22×D411yescharacteristic
329C2×C4×C107C2×#4111yescharacteristic
330C2×C4×C107C2×#4111yescharacteristic
331C2×C4×C107C2×#4111yescharacteristic
332C2×C4×C107H(5,𝔽2)11yescharacteristic
333C2×C4×C107H(5,𝔽2)11yescharacteristic
334C8×C107—22no—
335C8×C107—22no—
336C8×C107—41no—
337C8×C107—41no—
338C22×C107—22no—
339C22×C107—22no—
340C22×C107—22no—
341C22×C107—41no—
342C22×C107—41no—
343C22×C107—41no—
344C22×C107—41no—
345C22×C107—42no—
346C22×C107—42no—
347C22×C107—42no—
348C22×C107—42no—
349C22×C107—42no—
350C22×C107—42no—
351C22×C107—816no—
352C22×C107—81no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107—81no—
357C22×C107—81no—
358C22×C107—81no—
359C22×C107—81no—
360C22×C107—81no—
361C22×C107—81no—
362C22×C107—81no—
363C22×C107—81no—
364C22×C107—81no—
365C22×C107—81no—
366C22×C107—81no—
367C22×C107C2×#12111yescharacteristic
368C22×C107#52511yescharacteristic
369C22×C107#53511yescharacteristic
370C22×C107#57611yescharacteristic
371C22×C107#57611yescharacteristic
372C22×C107#57611yescharacteristic
373C22×C107#57711yescharacteristic
374C4×C107—22no—
375C4×C107—41no—
376C4×C107—41no—
377C4×C107—41no—
378C4×C107—41no—
379C4×C107—81no—
380C4×C107—81no—
381C4×C107—81no—
382C4×C107—81no—
383C4×C107—81no—
384C4×C107#54611yescharacteristic
385C4×C107#54611yescharacteristic
386C4×C107#55111yescharacteristic
387C4×C107#55111yescharacteristic
388#24512C10711yesmaximal, characteristic, direct product factor, Sylow
389C2×C107—42no—
390C2×C107—82no—
391C2×C107—82no—
392C2×C107—161no—
393C2×C107#241111yescharacteristic
394C2×C107#305811yescharacteristic
395C2×C107#306211yescharacteristic
396C2×C107#311811yescharacteristic
397C2×C107#312211yescharacteristic
398C2×C107#322011yescharacteristic
399C2×C107#322411yescharacteristic
400C2×#447C2×C10711yescharacteristic
401C2×#433C2×C10711yescharacteristic, complemented
402#2624C2×C10711yescharacteristic, complemented
403#2309C2×C10711yescharacteristic, complemented
404#2067C2×C10711yescharacteristic, complemented
405#2065C2×C10711yescharacteristic, complemented
406#2054C2×C10711yescharacteristic, complemented
407#2054C2×C10711yescharacteristic, complemented
408#1972C2×C10711yescharacteristic, complemented
409#1970C2×C10711yescharacteristic, complemented
410#1936C2×C10711yescharacteristic, complemented
411#1934C2×C10711yescharacteristic, complemented
412#1875C2×C10711yescharacteristic, complemented
413#1854C2×C10711yescharacteristic, complemented
414#1786C2×C10711yescharacteristic, complemented
415C107#2451211yescharacteristic, direct product factor, Sylow
416C23×D4C22×C10711yescharacteristic
417C22×D8C22×C10711yescharacteristic
418C22×D8C22×C10711yescharacteristic
419C2×#121C22×C10711yescharacteristic
420C2×#117C22×C10711yescharacteristic
421C2×#117C22×C10711yescharacteristic
422#447—24no—
423#433—24no—
424C2×#107C22×C10711yescharacteristic, complemented
425C2×#106C22×C10711yescharacteristic, complemented
426C2×C4⋊C8C22×C10711yescharacteristic, complemented
427C2×C4⋊C8C22×C10711yescharacteristic, complemented
428C2×#102C22×C10711yescharacteristic
429C2×#102C22×C10711yescharacteristic
430C2×#102C22×C10711yescharacteristic
431C2×#102C22×C10711yescharacteristic
432C2×#102C22×C10711yescharacteristic
433C2×#102C22×C10711yescharacteristic
434C2×#102C22×C10711yescharacteristic, complemented
435C2×#102C22×C10711yescharacteristic, complemented
436C2×C22⋊C8C22×C10711yescharacteristic
437C2×C22⋊C8C22×C10711yescharacteristic
438C2×#97C22×C10711yescharacteristic, complemented
439C2×C4×C8C22×C10711yescharacteristic, complemented
440#399—21no—
441#397—21no—
442#394—21no—
443#394—21no—
444#390—21no—
445#390—21no—
446#390C22×C10711yescharacteristic
447#390C22×C10711yescharacteristic
448#390C22×C10711yescharacteristic
449#390C22×C10711yescharacteristic
450#390C22×C10711yescharacteristic, complemented
451#390C22×C10711yescharacteristic, complemented
452#389C22×C10711yescharacteristic, complemented
453#389C22×C10711yescharacteristic, complemented
454#380C22×C10711yescharacteristic
455#379—21no—
456#379—21no—
457#340C22×C10711yescharacteristic, complemented
458#340C22×C10711yescharacteristic, complemented
459#340C22×C10711yescharacteristic, complemented
460#340C22×C10711yescharacteristic, complemented
461C25—21no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C23×C10711yescharacteristic
471C22×D4C23×C10711yescharacteristic
472C22×D4C23×C10711yescharacteristic
473C23×C4C23×C10711yescharacteristic
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—41no—
479C2×D8—41no—
480C22×C8C23×C10711yescharacteristic
481C22×C8C23×C10711yescharacteristic
482C22×C8C23×C10711yescharacteristic
483C22×C8C23×C10711yescharacteristic
484#121—22no—
485#121—22no—
486#117—22no—
487#117—22no—
488#117—41no—
489#117—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4D4×C10711yescharacteristic
493C2×C4⋊C4D4×C10711yescharacteristic
494C2×C4⋊C4C23×C10711yescharacteristic
495C2×C4⋊C4C23×C10711yescharacteristic
496C2×C4⋊C4C23×C10711yescharacteristic
497C2×C4⋊C4C23×C10711yescharacteristic
498C2×C4⋊C4C23×C10711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4D4×C10711yescharacteristic
515C2×C22⋊C4D4×C10711yescharacteristic
516C2×C42—21no—
517C2×C42C23×C10711yescharacteristic
518C2×C42C23×C10711yescharacteristic
519#107—41no—
520#106—41no—
521C4⋊C8—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529#102—41no—
530#102—41no—
531C22⋊C8—22no—
532C22⋊C8D4×C10714yes—
533#97—22no—
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—24no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24C2×D4×C10711yescharacteristic
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4#41×C10712yes—
576C2×D4#41×C10712yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4C2×D4×C10711yescharacteristic
587C22×C4C2×D4×C10711yescharacteristic
588C22×C4C2×D4×C10711yescharacteristic
589C22×C4C2×D4×C10711yescharacteristic
590C22×C4C2×D4×C10711yescharacteristic
591C22×C4C2×D4×C10712yes—
592C22×C4#41×C10712yes—
593C22×C4C24×C10711yescharacteristic
594D8—44no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8C2×D4×C10712yes—
607C2×C8C2×D4×C10712yes—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—81no—
621C4⋊C4—81no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—48no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23#121×C10712yes—
679C23C22×D4×C10711yescharacteristic
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4#121×C10712yes—
728C2×C4C22×D4×C10711yescharacteristic
729C2×C4C2×#41×C10711yescharacteristic
730C2×C4C2×#41×C10711yescharacteristic
731C2×C4C2×#41×C10711yescharacteristic
732C2×C4H(5,𝔽2)×C10711yescharacteristic
733C2×C4H(5,𝔽2)×C10711yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—816no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C10711yescharacteristic
768C22#525×C10711yescharacteristic
769C22#535×C10711yescharacteristic
770C22#576×C10711yescharacteristic
771C22#576×C10711yescharacteristic
772C22#576×C10711yescharacteristic
773C22#577×C10711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C10711yescharacteristic
785C4#546×C10711yescharacteristic
786C4#551×C10711yescharacteristic
787C4#551×C10711yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C107×#241111yescharacteristic
793C2C107×#305811yescharacteristic
794C2C107×#306211yescharacteristic
795C2C107×#311811yescharacteristic
796C2C107×#312211yescharacteristic
797C2C107×#322011yescharacteristic
798C2C107×#322411yescharacteristic
subgroupG/H
center, socleC23×C107C22×D4
commutator, Frattini, cosocleC22×C4C24×C107
prime radicalC2×#447×C107C2
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
2. C2×#433×C107C2semidirect
3. C107×#2624C2semidirect
4. C107×#2309C2semidirect
5. C107×#2067C2semidirect
6. C107×#2065C2semidirect
7. C107×#2054C2semidirect
8. C107×#2054C2semidirect
9. C107×#1972C2semidirect
10. C107×#1970C2semidirect
11. C107×#1936C2semidirect
12. C107×#1934C2semidirect
13. C107×#1875C2semidirect
14. C107×#1854C2semidirect
15. C107×#1786C2semidirect
24. C2×#107×C107C22semidirect
25. C2×#106×C107C22semidirect
26. C2×C4⋊C8×C107C22semidirect
27. C2×C4⋊C8×C107C22semidirect
34. C2×#102×C107C22semidirect
35. C2×#102×C107C22semidirect
38. C2×#97×C107C22semidirect
39. C2×C4×C8×C107C22semidirect
50. #390×C107C22semidirect
51. #390×C107C22semidirect
52. #389×C107C22semidirect
53. #389×C107C22semidirect
57. #340×C107C22semidirect
58. #340×C107C22semidirect
59. #340×C107C22semidirect
60. #340×C107C22semidirect
388. #24512C107direct (N × H)
401. C2×#433C2×C107semidirect
402. #2624C2×C107semidirect
403. #2309C2×C107semidirect
404. #2067C2×C107semidirect
405. #2065C2×C107semidirect
406. #2054C2×C107semidirect
407. #2054C2×C107semidirect
408. #1972C2×C107semidirect
409. #1970C2×C107semidirect
410. #1936C2×C107semidirect
411. #1934C2×C107semidirect
412. #1875C2×C107semidirect
413. #1854C2×C107semidirect
414. #1786C2×C107semidirect
415. C107#24512direct (N × H)
424. C2×#107C22×C107semidirect
425. C2×#106C22×C107semidirect
426. C2×C4⋊C8C22×C107semidirect
427. C2×C4⋊C8C22×C107semidirect
434. C2×#102C22×C107semidirect
435. C2×#102C22×C107semidirect
438. C2×#97C22×C107semidirect
439. C2×C4×C8C22×C107semidirect
450. #390C22×C107semidirect
451. #390C22×C107semidirect
452. #389C22×C107semidirect
453. #389C22×C107semidirect
457. #340C22×C107semidirect
458. #340C22×C107semidirect
459. #340C22×C107semidirect
460. #340C22×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1072
C2×#433×C1072
C107×#26242
C107×#23092
C107×#20672
C107×#20652
C107×#20542
C107×#19722
C107×#19702
C107×#19362
C107×#19342
C107×#18752
C107×#18542
C107×#17862
#24512107