Finite Group Databasebeta

← C103×#22058 #39927333

Subgroups — C103×#22058 #39927333

Order 26368.

976 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#448×C103C211yesmaximal, characteristic
2C103×#2324C211yesmaximal, characteristic
3C103×#2310C211yesmaximal, characteristic, complemented
4C103×#1973C211yesmaximal, characteristic, complemented
5C103×#1968C211yesmaximal, characteristic, complemented
6C103×#1935C211yesmaximal, characteristic, complemented
7C103×#1933C211yesmaximal, characteristic, complemented
8C103×#1928C211yesmaximal, characteristic, complemented
9C103×#1927C211yesmaximal, characteristic, complemented
10C103×#1877C211yesmaximal, characteristic, complemented
11C103×#1877C211yesmaximal, characteristic, complemented
12C103×#1875C211yesmaximal, characteristic
13C103×#1854C211yesmaximal, characteristic, complemented
14C103×#1787C211yesmaximal, characteristic, complemented
15C103×#1750C211yesmaximal, characteristic, complemented
16C23×Q8×C103C2211yescharacteristic
17C22×SD16×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C2×#121×C103C2211yescharacteristic
20C2×C4×D4×C103C2211yescharacteristic
21C2×#117×C103C2211yescharacteristic
22C2×#117×C103C2211yescharacteristic
23#448×C103C418yescomplemented
24C2×#107×C103C2211yescharacteristic
25C2×#106×C103C2211yescharacteristic
26C2×#103×C103C2211yescharacteristic
27C2×#103×C103C2211yescharacteristic
28C2×#103×C103C2211yescharacteristic
29C2×#103×C103C2211yescharacteristic
30C2×#103×C103C2211yescharacteristic
31C2×#103×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33C2×#102×C103C2211yescharacteristic
34C2×C22⋊C8×C103C2211yescharacteristic
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×#97×C103C2211yescharacteristic
37C2×C4×C8×C103C2211yescharacteristic
38#391×C103—21no—
39#391×C103—21no—
40#391×C103C2211yescharacteristic
41#391×C103C2211yescharacteristic
42#391×C103C2211yescharacteristic
43#391×C103C2211yescharacteristic
44#390×C103—21no—
45#390×C103C2211yescharacteristic
46#389×C103C2211yescharacteristic
47#388×C103—21no—
48#386×C103—21no—
49#385×C103—21no—
50#381×C103—21no—
51#381×C103—21no—
52#380×C103C2211yescharacteristic
53C4×C4⋊C4×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59#336×C103C2211yescharacteristic
60C22×Q8×C103—21no—
61C22×Q8×C103—22no—
62C22×Q8×C103—41no—
63C22×Q8×C103—41no—
64C22×Q8×C103—41no—
65C22×Q8×C103—41no—
66C22×Q8×C103C2×C414yescomplemented
67C22×Q8×C103C2311yescharacteristic
68C22×Q8×C103C2311yescharacteristic
69C22×D4×C103—21no—
70C22×D4×C103C2311yescharacteristic
71C23×C4×C103—21no—
72C23×C4×C103—21no—
73C23×C4×C103C2311yescharacteristic
74C2×SD16×C103—41no—
75C2×SD16×C103—41no—
76C2×SD16×C103—41no—
77C2×SD16×C103—41no—
78C2×SD16×C103C2×C414yes—
79C2×SD16×C103C2×C414yes—
80C22×C8×C103C2311yescharacteristic
81C22×C8×C103C2311yescharacteristic
82C22×C8×C103C2311yescharacteristic
83C22×C8×C103C2311yescharacteristic
84#121×C103—22no—
85#121×C103C2×C414yes—
86C4×D4×C103—41no—
87C4×D4×C103—41no—
88#117×C103—41no—
89#117×C103—41no—
90#117×C103—41no—
91#117×C103—41no—
92C2×C4⋊C4×C103—21no—
93C2×C4⋊C4×C103D411yescharacteristic
94C2×C4⋊C4×C103D411yescharacteristic
95C2×C4⋊C4×C103C2311yescharacteristic
96C2×C4⋊C4×C103C2311yescharacteristic
97C2×C4⋊C4×C103C2311yescharacteristic
98C2×C4⋊C4×C103C2311yescharacteristic
99C2×C4⋊C4×C103C2311yescharacteristic
100C2×C22⋊C4×C103—21no—
101C2×C22⋊C4×C103—21no—
102C2×C22⋊C4×C103—21no—
103C2×C22⋊C4×C103—21no—
104C2×C22⋊C4×C103—21no—
105C2×C22⋊C4×C103—21no—
106C2×C22⋊C4×C103D411yescharacteristic
107C2×C22⋊C4×C103D411yescharacteristic
108C2×C42×C103—21no—
109C2×C42×C103—21no—
110C2×C42×C103C2311yescharacteristic
111C2×C42×C103C2311yescharacteristic
112#107×C103—41no—
113#106×C103—41no—
114#103×C103—41no—
115#103×C103—41no—
116#103×C103—41no—
117#103×C103—41no—
118#103×C103C2×C414yescomplemented
119#103×C103C2×C414yescomplemented
120#102×C103—41no—
121#102×C103—41no—
122C22⋊C8×C103—22no—
123C22⋊C8×C103C2×C414yescomplemented
124#97×C103—41no—
125C4×C8×C103—41no—
126#95×C103—21no—
127#95×C103—21no—
128#95×C103—21no—
129#95×C103—21no—
130#95×C103—21no—
131#95×C103—21no—
132#95×C103—21no—
133#95×C103—21no—
134#95×C103—21no—
135#95×C103—21no—
136#95×C103—21no—
137C24×C103—21no—
138C24×C103C2×D411yescharacteristic
139C2×Q8×C103—24no—
140C2×Q8×C103—21no—
141C2×Q8×C103—21no—
142C2×Q8×C103—21no—
143C2×Q8×C103—21no—
144C2×Q8×C103—21no—
145C2×Q8×C103—21no—
146C2×Q8×C103—21no—
147C2×Q8×C103—21no—
148C2×Q8×C103—21no—
149C2×Q8×C103—21no—
150C2×Q8×C103—44no—
151C2×Q8×C103—44no—
152C2×Q8×C103—42no—
153C2×Q8×C103—42no—
154C2×Q8×C103—44no—
155C2×Q8×C103—44no—
156C2×Q8×C103C22×C412yes—
157C2×Q8×C103C22×C412yes—
158C2×D4×C103—24no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—21no—
162C2×D4×C103—21no—
163C2×D4×C103—21no—
164C2×D4×C103—81no—
165C2×D4×C103—81no—
166C2×D4×C103C22×C412yes—
167C22×C4×C103—21no—
168C22×C4×C103—21no—
169C22×C4×C103—21no—
170C22×C4×C103—21no—
171C22×C4×C103—24no—
172C22×C4×C103—21no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—42no—
180C22×C4×C103—42no—
181C22×C4×C103—42no—
182C22×C4×C103—81no—
183C22×C4×C103—81no—
184C22×C4×C103C22×C412yes—
185C22×C4×C103C2×D411yescharacteristic
186C22×C4×C103C2×D411yescharacteristic
187C22×C4×C103C2×D411yescharacteristic
188C22×C4×C103C2×D411yescharacteristic
189C22×C4×C103C2×D411yescharacteristic
190C22×C4×C103#4112yes—
191C22×C4×C103C2411yescharacteristic
192SD16×C103—44no—
193SD16×C103—44no—
194C2×C8×C103—21no—
195C2×C8×C103—21no—
196C2×C8×C103—21no—
197C2×C8×C103—21no—
198C2×C8×C103—21no—
199C2×C8×C103—21no—
200C2×C8×C103—21no—
201C2×C8×C103—21no—
202C2×C8×C103—21no—
203C2×C8×C103—21no—
204C2×C8×C103C22×C412yes—
205C2×C8×C103C22×C412yes—
206C4⋊C4×C103—21no—
207C4⋊C4×C103—21no—
208C4⋊C4×C103—21no—
209C4⋊C4×C103—21no—
210C4⋊C4×C103—21no—
211C4⋊C4×C103—21no—
212C4⋊C4×C103—21no—
213C4⋊C4×C103—21no—
214C4⋊C4×C103—21no—
215C4⋊C4×C103—41no—
216C4⋊C4×C103—41no—
217C4⋊C4×C103—81no—
218C4⋊C4×C103C22×C412yes—
219C22⋊C4×C103—24no—
220C22⋊C4×C103—41no—
221C22⋊C4×C103—41no—
222C22⋊C4×C103—42no—
223C22⋊C4×C103—42no—
224C22⋊C4×C103—81no—
225C22⋊C4×C103—81no—
226C22⋊C4×C103—81no—
227C42×C103—21no—
228C42×C103—21no—
229C42×C103—21no—
230C42×C103—21no—
231C42×C103—42no—
232C42×C103—81no—
233C23×C103—21no—
234C23×C103—21no—
235C23×C103—21no—
236C23×C103—21no—
237C23×C103—21no—
238C23×C103—21no—
239C23×C103—22no—
240C23×C103—41no—
241C23×C103—41no—
242C23×C103—41no—
243C23×C103—41no—
244C23×C103—41no—
245C23×C103—41no—
246C23×C103C4×D412yes—
247C23×C103C22×D411yescharacteristic
248Q8×C103—22no—
249Q8×C103—22no—
250Q8×C103—22no—
251Q8×C103—22no—
252Q8×C103—48no—
253Q8×C103—41no—
254Q8×C103—41no—
255Q8×C103—41no—
256Q8×C103—41no—
257D4×C103—22no—
258D4×C103—22no—
259D4×C103—41no—
260D4×C103—41no—
261D4×C103—84no—
262C2×C4×C103—21no—
263C2×C4×C103—21no—
264C2×C4×C103—22no—
265C2×C4×C103—22no—
266C2×C4×C103—22no—
267C2×C4×C103—22no—
268C2×C4×C103—22no—
269C2×C4×C103—22no—
270C2×C4×C103—22no—
271C2×C4×C103—21no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—21no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—21no—
279C2×C4×C103—21no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—21no—
283C2×C4×C103—48no—
284C2×C4×C103—41no—
285C2×C4×C103—41no—
286C2×C4×C103—41no—
287C2×C4×C103—41no—
288C2×C4×C103—41no—
289C2×C4×C103—41no—
290C2×C4×C103—41no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
301C2×C4×C103—41no—
302C2×C4×C103—84no—
303C2×C4×C103C4×D412yes—
304C2×C4×C103C23×C411yescharacteristic
305C2×C4×C103C2×#4111yescharacteristic
306C2×C4×C103H(5,𝔽2)11yescharacteristic
307C2×C4×C103H(5,𝔽2)11yescharacteristic
308C2×C4×C103H(5,𝔽2)11yescharacteristic
309C2×C4×C103H(5,𝔽2)11yescharacteristic
310C8×C103—22no—
311C8×C103—22no—
312C8×C103—41no—
313C8×C103—41no—
314C22×C103—22no—
315C22×C103—22no—
316C22×C103—22no—
317C22×C103—41no—
318C22×C103—41no—
319C22×C103—41no—
320C22×C103—41no—
321C22×C103—42no—
322C22×C103—42no—
323C22×C103—42no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—81no—
327C22×C103—81no—
328C22×C103C2×C4×D411yescharacteristic
329C22×C103#53411yescharacteristic
330C22×C103#53511yescharacteristic
331C22×C103#57711yescharacteristic
332C22×C103#57711yescharacteristic
333C22×C103#57711yescharacteristic
334C22×C103#57811yescharacteristic
335C4×C103—22no—
336C4×C103—42no—
337C4×C103—42no—
338C4×C103—41no—
339C4×C103—41no—
340C4×C103—41no—
341C4×C103—41no—
342C4×C103—42no—
343C4×C103—81no—
344C4×C103—81no—
345C4×C103—81no—
346C4×C103—81no—
347C4×C103#51811yescharacteristic
348C4×C103#51811yescharacteristic
349C4×C103#53811yescharacteristic
350C4×C103#53811yescharacteristic
351#22058C10311yesmaximal, characteristic, direct product factor, Sylow
352C2×C103—42no—
353C2×C103—82no—
354C2×C103#232111yescharacteristic
355C2×C103#294711yescharacteristic
356C2×C103#294911yescharacteristic
357C2×C103#320011yescharacteristic
358C2×C103#320111yescharacteristic
359C2×C103#322111yescharacteristic
360C2×C103#322511yescharacteristic
361C2×#448C2×C10311yescharacteristic
362#2324C2×C10311yescharacteristic
363#2310C2×C10311yescharacteristic, complemented
364#1973C2×C10311yescharacteristic, complemented
365#1968C2×C10311yescharacteristic, complemented
366#1935C2×C10311yescharacteristic, complemented
367#1933C2×C10311yescharacteristic, complemented
368#1928C2×C10311yescharacteristic, complemented
369#1927C2×C10311yescharacteristic, complemented
370#1877C2×C10311yescharacteristic, complemented
371#1877C2×C10311yescharacteristic, complemented
372#1875C2×C10311yescharacteristic
373#1854C2×C10311yescharacteristic, complemented
374#1787C2×C10311yescharacteristic, complemented
375#1750C2×C10311yescharacteristic, complemented
376C103#2205811yescharacteristic, direct product factor, Sylow
377C23×Q8C22×C10311yescharacteristic
378C22×SD16C22×C10311yescharacteristic
379C22×SD16C22×C10311yescharacteristic
380C2×#121C22×C10311yescharacteristic
381C2×C4×D4C22×C10311yescharacteristic
382C2×#117C22×C10311yescharacteristic
383C2×#117C22×C10311yescharacteristic
384#448C4×C10318yescomplemented
385C2×#107C22×C10311yescharacteristic
386C2×#106C22×C10311yescharacteristic
387C2×#103C22×C10311yescharacteristic
388C2×#103C22×C10311yescharacteristic
389C2×#103C22×C10311yescharacteristic
390C2×#103C22×C10311yescharacteristic
391C2×#103C22×C10311yescharacteristic
392C2×#103C22×C10311yescharacteristic
393C2×#102C22×C10311yescharacteristic
394C2×#102C22×C10311yescharacteristic
395C2×C22⋊C8C22×C10311yescharacteristic
396C2×C22⋊C8C22×C10311yescharacteristic
397C2×#97C22×C10311yescharacteristic
398C2×C4×C8C22×C10311yescharacteristic
399#391—21no—
400#391—21no—
401#391C22×C10311yescharacteristic
402#391C22×C10311yescharacteristic
403#391C22×C10311yescharacteristic
404#391C22×C10311yescharacteristic
405#390—21no—
406#390C22×C10311yescharacteristic
407#389C22×C10311yescharacteristic
408#388—21no—
409#386—21no—
410#385—21no—
411#381—21no—
412#381—21no—
413#380C22×C10311yescharacteristic
414C4×C4⋊C4C22×C10311yescharacteristic
415#340C22×C10311yescharacteristic
416#340C22×C10311yescharacteristic
417#340C22×C10311yescharacteristic
418#340C22×C10311yescharacteristic
419#336C22×C10311yescharacteristic
420#336C22×C10311yescharacteristic
421C22×Q8—21no—
422C22×Q8—22no—
423C22×Q8—41no—
424C22×Q8—41no—
425C22×Q8—41no—
426C22×Q8—41no—
427C22×Q8C2×C4×C10314yescomplemented
428C22×Q8C23×C10311yescharacteristic
429C22×Q8C23×C10311yescharacteristic
430C22×D4—21no—
431C22×D4C23×C10311yescharacteristic
432C23×C4—21no—
433C23×C4—21no—
434C23×C4C23×C10311yescharacteristic
435C2×SD16—41no—
436C2×SD16—41no—
437C2×SD16—41no—
438C2×SD16—41no—
439C2×SD16C2×C4×C10314yes—
440C2×SD16C2×C4×C10314yes—
441C22×C8C23×C10311yescharacteristic
442C22×C8C23×C10311yescharacteristic
443C22×C8C23×C10311yescharacteristic
444C22×C8C23×C10311yescharacteristic
445#121—22no—
446#121C2×C4×C10314yes—
447C4×D4—41no—
448C4×D4—41no—
449#117—41no—
450#117—41no—
451#117—41no—
452#117—41no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4D4×C10311yescharacteristic
455C2×C4⋊C4D4×C10311yescharacteristic
456C2×C4⋊C4C23×C10311yescharacteristic
457C2×C4⋊C4C23×C10311yescharacteristic
458C2×C4⋊C4C23×C10311yescharacteristic
459C2×C4⋊C4C23×C10311yescharacteristic
460C2×C4⋊C4C23×C10311yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4D4×C10311yescharacteristic
468C2×C22⋊C4D4×C10311yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C10311yescharacteristic
472C2×C42C23×C10311yescharacteristic
473#107—41no—
474#106—41no—
475#103—41no—
476#103—41no—
477#103—41no—
478#103—41no—
479#103C2×C4×C10314yescomplemented
480#103C2×C4×C10314yescomplemented
481#102—41no—
482#102—41no—
483C22⋊C8—22no—
484C22⋊C8C2×C4×C10314yescomplemented
485#97—41no—
486C4×C8—41no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C24—21no—
499C24C2×D4×C10311yescharacteristic
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8C22×C4×C10312yes—
518C2×Q8C22×C4×C10312yes—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4C22×C4×C10312yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4C22×C4×C10312yes—
546C22×C4C2×D4×C10311yescharacteristic
547C22×C4C2×D4×C10311yescharacteristic
548C22×C4C2×D4×C10311yescharacteristic
549C22×C4C2×D4×C10311yescharacteristic
550C22×C4C2×D4×C10311yescharacteristic
551C22×C4#41×C10312yes—
552C22×C4C24×C10311yescharacteristic
553SD16—44no—
554SD16—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8C22×C4×C10312yes—
566C2×C8C22×C4×C10312yes—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—81no—
579C4⋊C4C22×C4×C10312yes—
580C22⋊C4—24no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—81no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C4×D4×C10312yes—
608C23C22×D4×C10311yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—48no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—41no—
621D4—41no—
622D4—84no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—48no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4C4×D4×C10312yes—
665C2×C4C23×C4×C10311yescharacteristic
666C2×C4C2×#41×C10311yescharacteristic
667C2×C4H(5,𝔽2)×C10311yescharacteristic
668C2×C4H(5,𝔽2)×C10311yescharacteristic
669C2×C4H(5,𝔽2)×C10311yescharacteristic
670C2×C4H(5,𝔽2)×C10311yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×C4×D4×C10311yescharacteristic
690C22#534×C10311yescharacteristic
691C22#535×C10311yescharacteristic
692C22#577×C10311yescharacteristic
693C22#577×C10311yescharacteristic
694C22#577×C10311yescharacteristic
695C22#578×C10311yescharacteristic
696C4—22no—
697C4—42no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4#518×C10311yescharacteristic
709C4#518×C10311yescharacteristic
710C4#538×C10311yescharacteristic
711C4#538×C10311yescharacteristic
712C2—42no—
713C2—82no—
714C2C103×#232111yescharacteristic
715C2C103×#294711yescharacteristic
716C2C103×#294911yescharacteristic
717C2C103×#320011yescharacteristic
718C2C103×#320111yescharacteristic
719C2C103×#322111yescharacteristic
720C2C103×#322511yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC2×#121×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2310C2semidirect
4. C103×#1973C2semidirect
5. C103×#1968C2semidirect
6. C103×#1935C2semidirect
7. C103×#1933C2semidirect
8. C103×#1928C2semidirect
9. C103×#1927C2semidirect
10. C103×#1877C2semidirect
11. C103×#1877C2semidirect
13. C103×#1854C2semidirect
14. C103×#1787C2semidirect
15. C103×#1750C2semidirect
23. #448×C103C4semidirect
66. C22×Q8×C103C2×C4semidirect
118. #103×C103C2×C4semidirect
119. #103×C103C2×C4semidirect
123. C22⋊C8×C103C2×C4semidirect
351. #22058C103direct (N × H)
363. #2310C2×C103semidirect
364. #1973C2×C103semidirect
365. #1968C2×C103semidirect
366. #1935C2×C103semidirect
367. #1933C2×C103semidirect
368. #1928C2×C103semidirect
369. #1927C2×C103semidirect
370. #1877C2×C103semidirect
371. #1877C2×C103semidirect
373. #1854C2×C103semidirect
374. #1787C2×C103semidirect
375. #1750C2×C103semidirect
376. C103#22058direct (N × H)
384. #448C4×C103semidirect
427. C22×Q8C2×C4×C103semidirect
479. #103C2×C4×C103semidirect
480. #103C2×C4×C103semidirect
484. C22⋊C8C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1032
C103×#23242
C103×#23102
C103×#19732
C103×#19682
C103×#19352
C103×#19332
C103×#19282
C103×#19272
C103×#18772
C103×#18752
C103×#18542
C103×#17872
C103×#17502
#22058103