Finite Group Databasebeta

← C2×#11743351 #14262232

Subgroups — C2×#11743351 #14262232

Order 1792.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#533C211yesmaximal, characteristic, complemented
2#11743351C2132yesmaximal, direct product factor
3C2×D7×C4⋊Q8C211yesmaximal, characteristic, complemented
4C2×#90419C211yesmaximal, characteristic, complemented
5C2×#90419C211yesmaximal, characteristic, complemented
6C2×#90419C211yesmaximal, characteristic, complemented
7C2×#90385C212yesmaximal, complemented
8C2×#90376C212yesmaximal, complemented
9C2×#90330C212yesmaximal, complemented
10C2×#90319C212yesmaximal
11C2×#90332C212yesmaximal, complemented
12C2×#90316C212yesmaximal, complemented
13C2×#90272C212yesmaximal, complemented
14C2×#90274C212yesmaximal, complemented
15C2×#90263C212yesmaximal, complemented
16C2×#90260C212yesmaximal, complemented
17C2×#90224C212yesmaximal, complemented
18C2×#90220C212yesmaximal, complemented
19C2×#90161C211yesmaximal, characteristic, complemented
20C2×C4×#1157C211yesmaximal, characteristic
21C22×Q8×D7C2212yes—
22C22×#1157C2211yescharacteristic
23C7×#533C22116yescomplemented
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#125C2212yes—
27C2×C7×C22⋊Q8C2212yes—
28C2×C7×C22⋊Q8C2212yes—
29C2×C4×C7×Q8C2212yes—
30C2×C4×C7×Q8C2212yes—
31C2×C7×#117C2212yes—
32C22×C42×C7C2211yescharacteristic
33C2×#6509C2212yes—
34C2×#6509C2212yes—
35C2×#6509C2212yes—
36C2×Q8×Dic7C2212yes—
37C2×Q8×Dic7C2212yes—
38C2×Q8×Dic7C2212yes—
39C2×#6507C2212yes—
40C2×C4×C22⋊D7C2211yescharacteristic
41C2×C4×C22⋊D7C2211yescharacteristic
42C2×C4×C22⋊D7C2211yescharacteristic
43C2×C4×C22⋊D7C2211yescharacteristic
44C2×#6489C2211yescharacteristic
45C2×#6489C2212yes—
46C2×#6487C2212yes—
47C2×#6487C2212yes—
48#90419C22116yescomplemented
49#90419C22116yescomplemented
50#90419C22116yescomplemented
51D7×C4⋊Q8C22116yescomplemented
52#90385C22132yescomplemented
53#90376C22132yescomplemented
54#90332C22132yescomplemented
55#90330C22132yescomplemented
56#90319C22132yes—
57#90316C22132yescomplemented
58#90274C22132yescomplemented
59#90272C22132yescomplemented
60#90263C22132yescomplemented
61#90260C22132yescomplemented
62#90224C22132yescomplemented
63#90220C22132yescomplemented
64C2×#6461C2214yes—
65C2×#6460C2212yes—
66C2×#6460C2212yes—
67C2×#6460C2212yes—
68C2×#6457C2214yes—
69C2×#6455C2212yes—
70C2×#6455C2212yes—
71C2×#6455C2212yes—
72C2×#6455C2214yes—
73C2×D7×C4⋊C4C2212yes—
74C2×D7×C4⋊C4C2212yes—
75C2×#6453C2212yes—
76C2×#6453C2212yes—
77C2×#6453C2212yes—
78C2×#6453C2214yes—
79C2×#6452C2214yes—
80C2×#6452C2214yes—
81C2×#6451C2212yes—
82C2×#6451C2212yes—
83C2×#6451C2214yes—
84C2×#6450C2212yes—
85C2×#6450C2212yes—
86C2×#6450C2212yes—
87C2×#6450C2214yes—
88C2×#6448C2214yes—
89C2×#6446C2214yes—
90C2×#6442C2214yes—
91C2×#6442C2214yes—
92C2×#6439C2214yes—
93C4×#1157C22116yes—
94C2×C4×D28C2211yescharacteristic
95C2×C4×D28C2211yescharacteristic
96C2×#6435C2211yescharacteristic
97C2×#6435C2211yescharacteristic
98C2×#6435C2214yes—
99C2×C42×D7C2211yescharacteristic
100C2×C42×D7C2211yescharacteristic
101#90161C22116yescomplemented
102C2×#6433C2212yes—
103C2×#6433C2214yes—
104C2×#6432C2211yescharacteristic
105C2×#6432C2211yescharacteristic
106C2×C4×Dic14C2211yescharacteristic
107C2×C4×Dic14C2211yescharacteristic
108C2×C4×Dic14C2212yes—
109C2×C4×Dic14C2212yes—
110C2×C4×Dic14C2214yes—
111C2×#3509—71nomaximal, Sylow
112C22×C7×Q8C2312yes—
113C22×C7×Q8C2312yes—
114C23×C4×C7C2311yescharacteristic
115C23×C4×C7C2311yescharacteristic
116C23×C4×C7C2311yescharacteristic
117C22×C22⋊D7C2311yescharacteristic
118C22×C22⋊D7C2311yescharacteristic
119C2×Q8×D7—216no—
120C2×Q8×D7C23116yes—
121C2×#1157—28no—
122C2×#1157C2318yes—
123C22×D28C2311yescharacteristic
124C22×C4×D7C2311yescharacteristic
125C22×C4×D7C2311yescharacteristic
126C22×C4×D7C2311yescharacteristic
127C22×C4×D7C2311yescharacteristic
128C22×C4×D7C2311yescharacteristic
129C22×C4×D7C2314yes—
130C22×C4×D7C2311yescharacteristic
131C22×Dic14C2311yescharacteristic
132C22×Dic14C2312yes—
133C22×Dic14C2312yes—
134C22×Dic14C2314yes—
135C7×C4⋊Q8C2318yes—
136C7×C4⋊Q8C2318yes—
137C7×#125C23116yes—
138C7×C22⋊Q8C23116yes—
139C7×C22⋊Q8C23116yes—
140C4×C7×Q8C23116yes—
141C4×C7×Q8C23116yes—
142C7×#117C23116yes—
143C2×C7×C4⋊C4C2312yes—
144C2×C7×C4⋊C4C2314yes—
145C2×C7×C4⋊C4C2312yes—
146C2×C7×C4⋊C4C2312yes—
147C2×C7×C4⋊C4C2314yes—
148C2×C7×C4⋊C4C2312yes—
149C2×C7×C22⋊C4C2314yes—
150C2×C42×C7C2311yescharacteristic
151C2×C42×C7C2311yescharacteristic
152C2×C42×C7C2311yescharacteristic
153C2×C42×C7C2314yes—
154C2×C42×C7C2311yescharacteristic
155C2×C42×C7C2318yes—
156C2×C22⋊Dic7C2311yescharacteristic
157C2×C22⋊Dic7C2311yescharacteristic
158C2×C22⋊Dic7C2314yes—
159#6509C23116yes—
160#6509C23116yes—
161#6509C23116yes—
162Q8×Dic7C23116yes—
163Q8×Dic7C23116yes—
164Q8×Dic7C23116yes—
165#6507C23116yes—
166C4×C22⋊D7C2318yes—
167C4×C22⋊D7C2318yes—
168C4×C22⋊D7C2318yes—
169C4×C22⋊D7C2318yes—
170C2×(C2×D7)⋊C4C2311yescharacteristic
171C2×(C2×D7)⋊C4C2311yescharacteristic
172C2×(C2×D7)⋊C4C2311yescharacteristic
173C2×(C2×D7)⋊C4C2311yescharacteristic
174C2×(C2×D7)⋊C4C2314yes—
175C2×(C2×D7)⋊C4C2314yes—
176C2×(C2×D7)⋊C4C2314yes—
177#6489C23116yes—
178#6489C2318yes—
179C2×C4⋊Dic7C2312yes—
180C2×C4⋊Dic7C2312yes—
181C2×C4⋊Dic7C2311yescharacteristic
182C2×C4⋊Dic7C2311yescharacteristic
183C2×C4⋊Dic7C2314yes—
184C2×C4⋊Dic7C2312yes—
185C2×C4⋊Dic7C2312yes—
186C2×C4⋊Dic7C2314yes—
187C2×C4⋊Dic7C2314yes—
188#6487C23116yes—
189#6487C23116yes—
190C2×Dic7⋊C4C2311yescharacteristic
191C2×Dic7⋊C4C2314yes—
192C2×Dic7⋊C4C2311yescharacteristic
193C2×Dic7⋊C4C2314yes—
194C2×Dic7⋊C4C2311yescharacteristic
195C2×Dic7⋊C4C2311yescharacteristic
196C2×Dic7⋊C4C2314yes—
197C2×Dic7⋊C4C2314yes—
198C2×Dic7⋊C4C2314yes—
199C2×Dic7⋊C4C2314yes—
200C2×Dic7⋊C4C2314yes—
201C2×C4×Dic7C2314yes—
202C2×C4×Dic7C2311yescharacteristic
203C2×C4×Dic7C2311yescharacteristic
204C2×C4×Dic7C2311yescharacteristic
205C2×C4×Dic7C2311yescharacteristic
206C2×C4×Dic7C2314yes—
207C2×C4×Dic7C2314yes—
208C2×C4×Dic7C2311yescharacteristic
209C2×C4×Dic7C2311yescharacteristic
210C2×C4×Dic7C2314yes—
211#6461C23132yes—
212#6460C23116yes—
213#6460C23116yes—
214#6460C23116yes—
215#6457C23132yes—
216#6455C23116yes—
217#6455C23132yes—
218#6455C23116yes—
219#6455C23116yes—
220D7×C4⋊C4C23116yes—
221D7×C4⋊C4C23116yes—
222#6453C23116yes—
223#6453C23132yes—
224#6453C23116yes—
225#6453C23116yes—
226#6452C23132yes—
227#6452C23132yes—
228#6451C23116yes—
229#6451C23132yes—
230#6451C23116yes—
231#6450C23116yes—
232#6450C23116yes—
233#6450C23132yes—
234#6450C23116yes—
235#6448C23132yes—
236#6446C23132yes—
237#6442C23132yes—
238#6442C23132yes—
239#6439C23132yes—
240C4×D28C2318yes—
241C4×D28C2318yes—
242#6435C2318yes—
243#6435C2318yes—
244#6435C23132yes—
245C42×D7C2318yes—
246C42×D7C2318yes—
247#6433C23116yes—
248#6433C23132yes—
249#6432C2318yes—
250#6432C2318yes—
251C4×Dic14C2318yes—
252C4×Dic14C23116yes—
253C4×Dic14C23116yes—
254C4×Dic14C2318yes—
255C4×Dic14C23132yes—
256#3509—732no—
257C2×#557—72no—
258C2×#557—72no—
259C2×#556—72no—
260C2×#556—72no—
261C2×#552—72no—
262C2×#552—72no—
263C2×#552—72no—
264C2×#552—72no—
265C2×#541—72no—
266C2×#541—72no—
267C2×#536—72no—
268C2×#533—71no—
269C2×#533—71no—
270C2×#533—71no—
271C2×#533—71no—
272C2×#533D711yescharacteristic, complemented
273C22×C4⋊Q8—71no—
274C2×#519—72no—
275C2×C4×#41—71no—
276C24×C7C2411yescharacteristic
277C23×D7C2411yescharacteristic
278C23×D7C2411yescharacteristic
279C2×C7×Q8—28no—
280C2×C7×Q8—28no—
281C2×C7×Q8C2418yes—
282C2×C7×Q8C2418yes—
283C22×C4×C7—24no—
284C22×C4×C7—24no—
285C22×C4×C7—24no—
286C22×C4×C7C2411yescharacteristic
287C22×C4×C7C2414yes—
288C22×C4×C7C2414yes—
289C22×C4×C7C2411yescharacteristic
290C22×C4×C7C2411yescharacteristic
291C22×C4×C7C2414yes—
292C22×C4×C7C2414yes—
293C22×C4×C7C2414yes—
294C22×C4×C7C2411yescharacteristic
295C22×C4×C7C2411yescharacteristic
296C22×C4×C7C2411yescharacteristic
297C2×C22⋊D7—24no—
298C2×C22⋊D7—24no—
299C2×C22⋊D7C2414yes—
300C2×C22⋊D7C2414yes—
301C22×Dic7C2411yescharacteristic
302C22×Dic7C2411yescharacteristic
303C22×Dic7C2414yes—
304C22×Dic7C2411yescharacteristic
305C22×Dic7C2411yescharacteristic
306C22×Dic7C2411yescharacteristic
307C22×Dic7C2414yes—
308C22×Dic7C2411yescharacteristic
309Q8×D7—264no—
310#1157—232no—
311C2×D28—24no—
312C2×D28C2414yes—
313C2×C4×D7—216no—
314C2×C4×D7—24no—
315C2×C4×D7—24no—
316C2×C4×D7—24no—
317C2×C4×D7—24no—
318C2×C4×D7—24no—
319C2×C4×D7#4118yes—
320C2×C4×D7C2414yes—
321C2×C4×D7C2414yes—
322C2×C4×D7C2414yes—
323C2×C4×D7C2414yes—
324C2×C4×D7C2414yes—
325C2×C4×D7C24116yes—
326C2×C4×D7C2414yes—
327C2×Dic14—28no—
328C2×Dic14—28no—
329C2×Dic14—24no—
330C2×Dic14—216no—
331C2×Dic14C2414yes—
332C2×Dic14C2418yes—
333C2×Dic14C2418yes—
334C2×Dic14C24116yes—
335C7×C4⋊C4C2418yes—
336C7×C4⋊C4C24116yes—
337C7×C4⋊C4C2418yes—
338C7×C4⋊C4C2418yes—
339C7×C4⋊C4C24116yes—
340C7×C4⋊C4C2418yes—
341C7×C22⋊C4C24116yes—
342C42×C7C2414yes—
343C42×C7C2414yes—
344C42×C7C2414yes—
345C42×C7C24116yes—
346C42×C7C2414yes—
347C22⋊Dic7C2414yes—
348C22⋊Dic7C2414yes—
349C22⋊Dic7C24116yes—
350(C2×D7)⋊C4C2414yes—
351(C2×D7)⋊C4C2414yes—
352(C2×D7)⋊C4C2414yes—
353(C2×D7)⋊C4C2414yes—
354(C2×D7)⋊C4C24116yes—
355(C2×D7)⋊C4C24116yes—
356(C2×D7)⋊C4C24116yes—
357C4⋊Dic7C2418yes—
358C4⋊Dic7C2418yes—
359C4⋊Dic7C2414yes—
360C4⋊Dic7C2414yes—
361C4⋊Dic7C24116yes—
362C4⋊Dic7C2418yes—
363C4⋊Dic7C2418yes—
364C4⋊Dic7C24116yes—
365C4⋊Dic7C24116yes—
366Dic7⋊C4C2414yes—
367Dic7⋊C4C24116yes—
368Dic7⋊C4C2414yes—
369Dic7⋊C4C24116yes—
370Dic7⋊C4C2414yes—
371Dic7⋊C4C2414yes—
372Dic7⋊C4C24116yes—
373Dic7⋊C4C24116yes—
374Dic7⋊C4C24116yes—
375Dic7⋊C4C24116yes—
376Dic7⋊C4C24116yes—
377C4×Dic7C24116yes—
378C4×Dic7C2414yes—
379C4×Dic7C2414yes—
380C4×Dic7C2414yes—
381C4×Dic7C2414yes—
382C4×Dic7C24116yes—
383C4×Dic7C24116yes—
384C4×Dic7C2414yes—
385C4×Dic7C2414yes—
386C4×Dic7C24116yes—
387C22×#41—71no—
388C23×Q8—72no—
389#557—732no—
390#557—732no—
391#556—732no—
392#556—732no—
393#552—732no—
394#552—732no—
395#552—732no—
396#552—732no—
397#541—732no—
398#541—732no—
399#536—732no—
400#533—716no—
401#533—716no—
402#533—716no—
403#533—716no—
404#533C2×D7116yescomplemented
405C2×C4⋊Q8—72no—
406C2×C4⋊Q8—716no—
407C2×C4⋊Q8—72no—
408C2×C4⋊Q8—72no—
409C2×C4⋊Q8—74no—
410C2×C4⋊Q8—71no—
411C2×C4⋊Q8—71no—
412C2×C4⋊Q8C2×D711yescharacteristic
413C2×C4⋊Q8C2×D711yescharacteristic
414C2×#126—74no—
415C2×#126—74no—
416C2×#126—74no—
417C2×#126—74no—
418C2×#125—74no—
419C2×#125—74no—
420C2×#125—72no—
421C2×#125—72no—
422C2×#125—72no—
423C2×#125—74no—
424C2×#125—72no—
425C2×#125—74no—
426C2×#125C2×D712yes—
427C2×#124—74no—
428C2×#123—74no—
429C2×#123—74no—
430C2×C22⋊Q8—72no—
431C2×C22⋊Q8—72no—
432C2×C22⋊Q8—72no—
433C2×C22⋊Q8—72no—
434C2×C22⋊Q8—72no—
435C2×C22⋊Q8—72no—
436C2×C22⋊Q8—72no—
437C2×C22⋊Q8—72no—
438C2×C22⋊Q8C2×D712yes—
439C2×C22⋊Q8C2×D712yes—
440#519—732no—
441C4×#41—716no—
442C2×C4×Q8—72no—
443C2×C4×Q8—72no—
444C2×C4×Q8—72no—
445C2×C4×Q8—72no—
446C2×C4×Q8—74no—
447C2×C4×Q8—72no—
448C2×C4×Q8—72no—
449C2×C4×Q8—71no—
450C2×C4×Q8—71no—
451C2×C4×Q8—72no—
452C2×C4×Q8—74no—
453C2×C4×Q8—72no—
454C2×C4×Q8C2×D712yes—
455C2×C4×Q8C2×D712yes—
456C2×C4×D4—71no—
457C2×C4×D4—71no—
458C2×C4×D4—71no—
459C2×C4×D4—71no—
460C2×C4×D4—71no—
461C2×C4×D4—71no—
462C2×#117—71no—
463C2×#117—72no—
464C2×#117—72no—
465C2×#117—74no—
466C2×#117—72no—
467C2×#117—72no—
468C2×#117—71no—
469C2×#117—71no—
470C2×#117—74no—
471C2×#117C2×D712yes—
472C22×C4⋊C4—72no—
473C22×C4⋊C4—72no—
474C22×C42—71no—
475C22×C42—71no—
476C22×C42C2×D711yescharacteristic
477C23×C7—22no—
478C23×C7—22no—
479C23×C7—22no—
480C23×C7C2512yes—
481C23×C7C2511yescharacteristic
482C22×D7—22no—
483C22×D7—22no—
484C22×D7—22no—
485C22×D7—22no—
486C22×D7—22no—
487C22×D7C2×#4114yes—
488C22×D7C2512yes—
489C22×D7C2512yes—
490C7×Q8—216no—
491C7×Q8—216no—
492C2×C4×C7—28no—
493C2×C4×C7—22no—
494C2×C4×C7—22no—
495C2×C4×C7—22no—
496C2×C4×C7—28no—
497C2×C4×C7—28no—
498C2×C4×C7—28no—
499C2×C4×C7—28no—
500C2×C4×C7C2×#4114yes—
501C2×C4×C72−1+414yes—
502C2×C4×C72−1+414yes—
503C2×C4×C7C2512yes—
504C2×C4×C7C2518yes—
505C2×C4×C7C2518yes—
506C2×C4×C7C2512yes—
507C2×C4×C7C2512yes—
508C2×C4×C7C2512yes—
509C2×C4×C7C2512yes—
510C2×C4×C7C2512yes—
511C22⋊D7—28no—
512C22⋊D7—28no—
513C2×Dic7—28no—
514C2×Dic7—22no—
515C2×Dic7—28no—
516C2×Dic7—22no—
517C2×Dic7—22no—
518C2×Dic7—22no—
519C2×Dic7—22no—
520C2×Dic7C2×#4114yes—
521C2×Dic7C2512yes—
522C2×Dic7C2512yes—
523C2×Dic7C2518yes—
524C2×Dic7C2512yes—
525C2×Dic7C2512yes—
526C2×Dic7C2512yes—
527C2×Dic7C2518yes—
528C2×Dic7C2512yes—
529D28—28no—
530C4×D7—232no—
531C4×D7—28no—
532C4×D7—28no—
533C4×D7—28no—
534C4×D7—28no—
535C4×D7—28no—
536C4×D7C2×#41116yes—
537Dic14—216no—
538Dic14—216no—
539Dic14—28no—
540Dic14—232no—
541C2×#41—78no—
542C2×#41—148no—
543C22×Q8—716no—
544C22×Q8—72no—
545C22×Q8—72no—
546C22×Q8—74no—
547C22×Q8—71no—
548C22×Q8—1416no—
549C22×Q8C22×D712yes—
550C22×Q8C22×D712yes—
551C22×D4—71no—
552C22×D4—71no—
553C22×D4—71no—
554C23×C4—71no—
555C23×C4—74no—
556C23×C4—71no—
557C23×C4—71no—
558C23×C4—71no—
559C23×C4—71no—
560C23×C4—71no—
561C23×C4C22×D711yescharacteristic
562C23×C4C22×D711yescharacteristic
563C23×C4C22×D711yescharacteristic
564C4⋊Q8—716no—
565C4⋊Q8—716no—
566C4⋊Q8—716no—
567C4⋊Q8—732no—
568C4⋊Q8—78no—
569C4⋊Q8—78no—
570C4⋊Q8C22×D718yes—
571C4⋊Q8C22×D718yes—
572#126—732no—
573#126—732no—
574#126—732no—
575#126—732no—
576#125—716no—
577#125—716no—
578#125—716no—
579#125—732no—
580#125—732no—
581#125—732no—
582#125—716no—
583#125—732no—
584#125C22×D7116yes—
585#124—732no—
586#123—732no—
587#123—732no—
588C22⋊Q8—716no—
589C22⋊Q8—716no—
590C22⋊Q8—716no—
591C22⋊Q8—716no—
592C22⋊Q8—716no—
593C22⋊Q8—716no—
594C22⋊Q8—716no—
595C22⋊Q8—716no—
596C22⋊Q8C22×D7116yes—
597C22⋊Q8C22×D7116yes—
598C4×Q8—716no—
599C4×Q8—716no—
600C4×Q8—716no—
601C4×Q8—716no—
602C4×Q8—732no—
603C4×Q8—716no—
604C4×Q8—716no—
605C4×Q8—78no—
606C4×Q8—78no—
607C4×Q8—716no—
608C4×Q8—732no—
609C4×Q8—716no—
610C4×Q8C22×D7116yes—
611C4×Q8C22×D7116yes—
612C4×D4—78no—
613C4×D4—78no—
614C4×D4—78no—
615C4×D4—78no—
616C4×D4—78no—
617C4×D4—78no—
618#117—78no—
619#117—716no—
620#117—716no—
621#117—732no—
622#117—716no—
623#117—716no—
624#117—78no—
625#117—78no—
626#117—732no—
627#117C22×D7116yes—
628C2×C4⋊C4—72no—
629C2×C4⋊C4—72no—
630C2×C4⋊C4—74no—
631C2×C4⋊C4—74no—
632C2×C4⋊C4—72no—
633C2×C4⋊C4—71no—
634C2×C4⋊C4—71no—
635C2×C4⋊C4—71no—
636C2×C4⋊C4—71no—
637C2×C4⋊C4—71no—
638C2×C4⋊C4—71no—
639C2×C4⋊C4—72no—
640C2×C4⋊C4—74no—
641C2×C4⋊C4—74no—
642C2×C4⋊C4—74no—
643C2×C4⋊C4—74no—
644C2×C4⋊C4—74no—
645C2×C4⋊C4—74no—
646C2×C4⋊C4—74no—
647C2×C4⋊C4—74no—
648C2×C4⋊C4—716no—
649C2×C4⋊C4—716no—
650C2×C4⋊C4C22×D712yes—
651C2×C4⋊C4C22×D712yes—
652C2×C4⋊C4C22×D712yes—
653C2×C4⋊C4C22×D712yes—
654C2×C4⋊C4C22×D714yes—
655C2×C4⋊C4C22×D714yes—
656C2×C22⋊C4—71no—
657C2×C22⋊C4—71no—
658C2×C22⋊C4—74no—
659C2×C22⋊C4—71no—
660C2×C22⋊C4—71no—
661C2×C22⋊C4—74no—
662C2×C22⋊C4—71no—
663C2×C22⋊C4—71no—
664C2×C22⋊C4—74no—
665C2×C22⋊C4—74no—
666C2×C22⋊C4C22×D714yes—
667C2×C42—71no—
668C2×C42—74no—
669C2×C42—74no—
670C2×C42—74no—
671C2×C42—71no—
672C2×C42—74no—
673C2×C42—71no—
674C2×C42—71no—
675C2×C42—71no—
676C2×C42—71no—
677C2×C42—78no—
678C2×C42—78no—
679C2×C42C22×D711yescharacteristic
680C2×C42C22×D714yes—
681C2×C42C22×D711yescharacteristic
682C2×C42C22×D711yescharacteristic
683C2×C42C22×D718yes—
684C2×C42C22×D711yescharacteristic
685C22×C7—22no—
686C22×C7—22no—
687C22×C7—22no—
688C22×C7—44no—
689C22×C7C22×#4112yes—
690C22×C7C2×2−1+412yes—
691C22×C7C2×2−1+412yes—
692C22×C7C2611yescharacteristic
693C2×D7—22no—
694C2×D7—22no—
695C2×D7—28no—
696C2×D7—22no—
697C2×D7—22no—
698C2×D7—22no—
699C2×D7—44no—
700C2×D7C22×#4114yes—
701C4×C7—28no—
702C4×C7—22no—
703C4×C7—22no—
704C4×C7—22no—
705C4×C7—28no—
706C4×C7C22×#4114yes—
707C4×C7C2×2−1+414yes—
708C4×C7C2×2−1+414yes—
709Dic7—28no—
710Dic7—22no—
711Dic7—28no—
712Dic7—22no—
713Dic7—22no—
714Dic7—22no—
715Dic7—22no—
716Dic7C22×#4114yes—
717C24—71no—
718C24—71no—
719C24C23×D711yescharacteristic
720#41—1432no—
721C2×Q8—28no—
722C2×Q8—28no—
723C2×Q8—78no—
724C2×Q8—78no—
725C2×Q8—716no—
726C2×Q8—74no—
727C2×Q8—1416no—
728C2×Q8—144no—
729C2×Q8—1464no—
730C2×Q8—148no—
731C2×Q8—148no—
732C2×Q8C23×D718yes—
733C2×Q8C23×D718yes—
734C2×D4—74no—
735C2×D4—74no—
736C2×D4—74no—
737C2×D4—144no—
738C2×D4—144no—
739C2×D4—144no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—71no—
744C22×C4—78no—
745C22×C4—74no—
746C22×C4—71no—
747C22×C4—71no—
748C22×C4—74no—
749C22×C4—71no—
750C22×C4—71no—
751C22×C4—74no—
752C22×C4—71no—
753C22×C4—74no—
754C22×C4—74no—
755C22×C4—74no—
756C22×C4—74no—
757C22×C4—74no—
758C22×C4—716no—
759C22×C4—1416no—
760C22×C4—144no—
761C22×C4—144no—
762C22×C4—144no—
763C22×C4—144no—
764C22×C4—144no—
765C22×C4C23×D714yes—
766C22×C4C23×D714yes—
767C22×C4C23×D714yes—
768C22×C4C23×D711yescharacteristic
769C22×C4C23×D714yes—
770C22×C4C23×D714yes—
771C22×C4C23×D711yescharacteristic
772C22×C4C23×D711yescharacteristic
773C22×C4C23×D711yescharacteristic
774C22×C4C23×D711yescharacteristic
775C22×C4C23×D711yescharacteristic
776C4⋊C4—716no—
777C4⋊C4—716no—
778C4⋊C4—74no—
779C4⋊C4—74no—
780C4⋊C4—74no—
781C4⋊C4—74no—
782C4⋊C4—716no—
783C4⋊C4—716no—
784C4⋊C4—716no—
785C4⋊C4—716no—
786C4⋊C4—716no—
787C4⋊C4—78no—
788C4⋊C4—78no—
789C4⋊C4—78no—
790C4⋊C4—74no—
791C4⋊C4—74no—
792C4⋊C4—78no—
793C4⋊C4—716no—
794C4⋊C4—716no—
795C4⋊C4—716no—
796C4⋊C4C23×D718yes—
797C4⋊C4C23×D718yes—
798C4⋊C4C23×D718yes—
799C4⋊C4C23×D718yes—
800C4⋊C4C23×D7116yes—
801C4⋊C4C23×D7116yes—
802C22⋊C4—74no—
803C22⋊C4—74no—
804C22⋊C4—716no—
805C22⋊C4—74no—
806C22⋊C4—74no—
807C22⋊C4—716no—
808C22⋊C4—74no—
809C22⋊C4—74no—
810C22⋊C4—716no—
811C22⋊C4—716no—
812C22⋊C4C23×D7116yes—
813C42—74no—
814C42—74no—
815C42—74no—
816C42—74no—
817C42—74no—
818C42—74no—
819C42—716no—
820C42—716no—
821C42—716no—
822C42—716no—
823C42C23×D714yes—
824C42C23×D714yes—
825C42C23×D714yes—
826C42C23×D714yes—
827C42C23×D7116yes—
828C2×C7—42no—
829C2×C7#350914yescomplemented
830C2×C7C23×#4111yescharacteristic
831C2×C7C22×2−1+411yescharacteristic
832C2×C7C22×2−1+411yescharacteristic
833D7—24no—
834D7—42no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—72no—
839C23—74no—
840C23—72no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23—142no—
845C23—142no—
846C23C24×D712yes—
847C23C24×D711yescharacteristic
848Q8—216no—
849Q8—216no—
850Q8—1432no—
851Q8—148no—
852Q8—1416no—
853Q8—1416no—
854D4—148no—
855D4—148no—
856D4—148no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—72no—
866C2×C4—74no—
867C2×C4—716no—
868C2×C4—72no—
869C2×C4—72no—
870C2×C4—78no—
871C2×C4—72no—
872C2×C4—72no—
873C2×C4—78no—
874C2×C4—72no—
875C2×C4—1432no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—148no—
879C2×C4—142no—
880C2×C4—148no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—148no—
884C2×C4—148no—
885C2×C4—148no—
886C2×C4—148no—
887C2×C4—148no—
888C2×C4#655114yes—
889C2×C4D7×#4114yes—
890C2×C4#655414yes—
891C2×C4C24×D712yes—
892C2×C4C24×D718yes—
893C2×C4C24×D718yes—
894C2×C4C24×D712yes—
895C2×C4C24×D712yes—
896C2×C4C24×D712yes—
897C2×C4C24×D712yes—
898C2×C4C24×D712yes—
899C7C2×#350911yescharacteristic, complemented, Sylow
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—74no—
905C22—142no—
906C22—142no—
907C22—148no—
908C22—142no—
909C22—142no—
910C22—142no—
911C22—284no—
912C22C2×#655112yes—
913C22C2×D7×#4112yes—
914C22C2×#655412yes—
915C22C25×D711yescharacteristic
916C4—22no—
917C4—22no—
918C4—28no—
919C4—22no—
920C4—28no—
921C4—74no—
922C4—142no—
923C4—142no—
924C4—148no—
925C4—142no—
926C4—142no—
927C4—142no—
928C4—148no—
929C4C2×#655114yes—
930C4C2×D7×#4114yes—
931C4C2×#655414yes—
932C2—42no—
933C2—144no—
934C2—282no—
935C2#1174335114yesdirect product factor
936C2C22×#655111yescharacteristic
937C2C22×#655411yescharacteristic
938C2C22×D7×#4111yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#533C2
socleC23×C7C25
prime radicalC22×#1157C22
hypercenterC2×#533D7
hypocenterC7C2×#3509
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×C7×#533C2semidirect
2. #11743351C2direct (N × H)
3. C2×D7×C4⋊Q8C2semidirect
4. C2×#90419C2semidirect
5. C2×#90419C2semidirect
6. C2×#90419C2semidirect
7. C2×#90385C2semidirect
8. C2×#90376C2semidirect
9. C2×#90330C2semidirect
11. C2×#90332C2semidirect
12. C2×#90316C2semidirect
13. C2×#90272C2semidirect
14. C2×#90274C2semidirect
15. C2×#90263C2semidirect
16. C2×#90260C2semidirect
17. C2×#90224C2semidirect
18. C2×#90220C2semidirect
19. C2×#90161C2semidirect
23. C7×#533C22semidirect
48. #90419C22semidirect
49. #90419C22semidirect
50. #90419C22semidirect
51. D7×C4⋊Q8C22semidirect
52. #90385C22semidirect
53. #90376C22semidirect
54. #90332C22semidirect
55. #90330C22semidirect
57. #90316C22semidirect
58. #90274C22semidirect
59. #90272C22semidirect
60. #90263C22semidirect
61. #90260C22semidirect
62. #90224C22semidirect
63. #90220C22semidirect
101. #90161C22semidirect
272. C2×#533D7semidirect
404. #533C2×D7semidirect
829. C2×C7#3509semidirect
899. C7C2×#3509semidirect
935. C2#11743351direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5332
#117433512
C2×D7×C4⋊Q82
C2×#904192
C2×#903852
C2×#903762
C2×#903302
C2×#903192
C2×#903322
C2×#903162
C2×#902722
C2×#902742
C2×#902632
C2×#902602
C2×#902242
C2×#902202
C2×#901612
C2×C4×#11572
C2×#35097