Finite Group Databasebeta

← C2×C7×#3343 #13238451

Subgroups — C2×C7×#3343 #13238451

Order 1792.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#552C211yesmaximal, characteristic, complemented
2C2×C7×#547C211yesmaximal, characteristic
3C7×#3343C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#484C211yesmaximal, characteristic, complemented
6C2×C7×#482C211yesmaximal, characteristic, complemented
7C2×C7×#483C211yesmaximal, characteristic, complemented
8C2×C7×#480C211yesmaximal, characteristic, complemented
9C2×C7×#477C211yesmaximal, characteristic, complemented
10C2×C7×#478C211yesmaximal, characteristic, complemented
11C2×C7×#468C211yesmaximal, characteristic, complemented
12C2×C7×#465C211yesmaximal, characteristic, complemented
13C2×C7×#440C211yesmaximal, characteristic, complemented
14C2×C7×#435C211yesmaximal, characteristic, complemented
15C2×C7×#428C211yesmaximal, characteristic, complemented
16C22×C7×#107C211yesmaximal, characteristic, complemented
17C22×C7×#41—21no—
18C22×C7×SD16C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C23×C7×C8C2211yescharacteristic
21C7×#552—24no—
22C7×#552C2218yescomplemented
23C7×#547—24no—
24C7×#547C2218yes—
25C2×C7×C4⋊Q8C2211yescharacteristic
26C2×C7×#126—21no—
27C2×C7×#125—21no—
28C2×C7×#125C2211yescharacteristic
29C2×C7×#123—21no—
30C2×C7×#123—21no—
31C2×C7×#123—21no—
32C2×C7×C22⋊Q8—21no—
33C2×C7×C22⋊Q8C2211yescharacteristic
34C2×C7×C22⋊Q8C2211yescharacteristic
35C2×C7×#121C2211yescharacteristic
36C2×C7×#121C2211yescharacteristic
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×D4C2211yescharacteristic
39C2×C4×C7×D4C2211yescharacteristic
40C2×C7×#117—21no—
41C2×C7×#117C2211yescharacteristic
42C22×C7×C4⋊C4C2211yescharacteristic
43C22×C7×C4⋊C4C2211yescharacteristic
44C22×C7×C4⋊C4C2211yescharacteristic
45C7×#501C2218yescomplemented
46C7×#484C2218yescomplemented
47C7×#483C2218yescomplemented
48C7×#482C2218yescomplemented
49C7×#480C2218yescomplemented
50C7×#478C2218yescomplemented
51C7×#477C2218yescomplemented
52C7×#468C2218yescomplemented
53C7×#465C2218yescomplemented
54C7×#440C2218yescomplemented
55C7×#435C2218yescomplemented
56C7×#428C2218yescomplemented
57C2×C7×#107C2211yescharacteristic
58C2×C7×#107C2211yescharacteristic
59C2×C7×#107C2211yescharacteristic
60C2×C7×#107C2211yescharacteristic
61C2×C7×#107C2211yescharacteristic
62C2×C7×#107C2211yescharacteristic
63C2×C7×#107C2218yescomplemented
64C2×C7×#106C2211yescharacteristic
65C2×C7×#106C2211yescharacteristic
66C2×C7×#106C2211yescharacteristic
67C2×C7×C4⋊C8C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#103C2211yescharacteristic
70C2×C7×#103C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×#102C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×C22⋊C8C2211yescharacteristic
76C2×C7×#97C2211yescharacteristic
77C2×#3343C711yesmaximal, characteristic, direct product factor, Sylow
78C2×C7×#41—28no—
79C2×C7×#41—48no—
80C22×C7×Q8—21no—
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4—21no—
83C22×C7×D4—21no—
84C22×C7×D4D411yescharacteristic
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7—21no—
87C23×C4×C7—21no—
88C23×C4×C7—21no—
89C23×C4×C7—21no—
90C23×C4×C7C2311yescharacteristic
91C23×C4×C7C2311yescharacteristic
92C2×C7×SD16—24no—
93C2×C7×SD16C2314yes—
94C2×C7×M16—24no—
95C2×C7×M16C2314yes—
96C22×C7×C8—24no—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2314yes—
101C22×C7×C8C2311yescharacteristic
102C7×C4⋊Q8—22no—
103C7×C4⋊Q8C2314yes—
104C7×#126—28no—
105C7×#125—28no—
106C7×#125—22no—
107C7×#125C2314yes—
108C7×#123—28no—
109C7×#123—28no—
110C7×#123—28no—
111C7×C22⋊Q8—22no—
112C7×C22⋊Q8—22no—
113C7×C22⋊Q8—28no—
114C7×C22⋊Q8C2314yes—
115C7×C22⋊Q8C2314yes—
116C7×#121—22no—
117C7×#121—22no—
118C7×#121C2314yes—
119C7×#121C2314yes—
120C4×C7×Q8—22no—
121C4×C7×Q8C2314yes—
122C4×C7×D4—22no—
123C4×C7×D4D414yes—
124C4×C7×D4C2314yes—
125C4×C7×D4C2314yes—
126C7×#117—22no—
127C7×#117—28no—
128C7×#117C2314yes—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—22no—
133C2×C7×C4⋊C4—22no—
134C2×C7×C4⋊C4—22no—
135C2×C7×C4⋊C4—21no—
136C2×C7×C4⋊C4—21no—
137C2×C7×C4⋊C4—21no—
138C2×C7×C4⋊C4—21no—
139C2×C7×C4⋊C4—21no—
140C2×C7×C4⋊C4—21no—
141C2×C7×C4⋊C4D411yescharacteristic
142C2×C7×C4⋊C4C2314yes—
143C2×C7×C4⋊C4C2314yes—
144C2×C7×C4⋊C4C2314yes—
145C2×C7×C4⋊C4C2311yescharacteristic
146C2×C7×C4⋊C4C2311yescharacteristic
147C2×C7×C4⋊C4C2311yescharacteristic
148C2×C7×C4⋊C4C2311yescharacteristic
149C2×C7×C4⋊C4C2311yescharacteristic
150C2×C7×C4⋊C4C2311yescharacteristic
151C2×C7×C22⋊C4—21no—
152C2×C7×C22⋊C4—21no—
153C2×C7×C22⋊C4—21no—
154C2×C7×C22⋊C4—21no—
155C2×C7×C22⋊C4—21no—
156C2×C7×C22⋊C4—21no—
157C2×C7×C22⋊C4D411yescharacteristic
158C2×C7×C22⋊C4D411yescharacteristic
159C2×C42×C7—21no—
160C2×C42×C7—21no—
161C2×C42×C7C2311yescharacteristic
162C7×#107C2314yes—
163C7×#107C2314yes—
164C7×#107C2314yes—
165C7×#107C2314yes—
166C7×#107C2314yes—
167C7×#107C2314yes—
168C7×#106C2314yes—
169C7×#106C2314yes—
170C7×#106C2314yes—
171C7×C4⋊C8C2314yes—
172C7×#103C2314yes—
173C7×#103C2314yes—
174C7×#103C2314yes—
175C7×#102C2314yes—
176C7×#102C2314yes—
177C7×#102C2314yes—
178C7×C22⋊C8C2314yes—
179C7×C22⋊C8C2314yes—
180C7×#97C2314yes—
181C2×#552C2×C711yescharacteristic, complemented
182C2×#547C2×C711yescharacteristic
183#3343C2×C7116yesdirect product factor
184C2×#501C2×C711yescharacteristic, complemented
185C2×#484C2×C711yescharacteristic, complemented
186C2×#482C2×C711yescharacteristic, complemented
187C2×#483C2×C711yescharacteristic, complemented
188C2×#480C2×C711yescharacteristic, complemented
189C2×#477C2×C711yescharacteristic, complemented
190C2×#478C2×C711yescharacteristic, complemented
191C2×#468C2×C711yescharacteristic, complemented
192C2×#465C2×C711yescharacteristic, complemented
193C2×#440C2×C711yescharacteristic, complemented
194C2×#435C2×C711yescharacteristic, complemented
195C2×#428C2×C711yescharacteristic, complemented
196C22×#107C2×C711yescharacteristic, complemented
197C24×C7—21no—
198C24×C7C2×D411yescharacteristic
199C24×C7C2×D411yescharacteristic
200C7×#41—432no—
201C2×C7×Q8—21no—
202C2×C7×Q8—24no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—44no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
209C2×C7×D4—24no—
210C2×C7×D4—21no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—44no—
214C2×C7×D4—44no—
215C2×C7×D4C2×D414yes—
216C2×C7×D4C2412yes—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—24no—
222C22×C4×C7—24no—
223C22×C4×C7—24no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—24no—
232C22×C4×C7—44no—
233C22×C4×C7—44no—
234C22×C4×C7—44no—
235C22×C4×C7—44no—
236C22×C4×C7C2×D412yes—
237C22×C4×C7C2×D412yes—
238C22×C4×C7C2×D411yescharacteristic
239C22×C4×C7C2×D411yescharacteristic
240C22×C4×C7C2×D411yescharacteristic
241C22×C4×C7C2×D411yescharacteristic
242C22×C4×C7C2412yes—
243C22×C4×C7C2412yes—
244C22×C4×C7C2411yescharacteristic
245C7×SD16—28no—
246C7×M16—28no—
247C2×C7×C8—22no—
248C2×C7×C8—22no—
249C2×C7×C8—22no—
250C2×C7×C8—28no—
251C2×C7×C8#4114yescomplemented
252C2×C7×C8C2412yes—
253C2×C7×C8C2412yes—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—21no—
260C7×C4⋊C4—24no—
261C7×C4⋊C4—24no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—24no—
264C7×C4⋊C4—24no—
265C7×C4⋊C4—24no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4—24no—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—24no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4C2×D414yes—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C4⋊C4C2412yes—
277C7×C4⋊C4C2412yes—
278C7×C22⋊C4—24no—
279C7×C22⋊C4—24no—
280C7×C22⋊C4—24no—
281C7×C22⋊C4—24no—
282C7×C22⋊C4—24no—
283C7×C22⋊C4—24no—
284C7×C22⋊C4C2×D414yes—
285C7×C22⋊C4C2×D414yes—
286C42×C7—24no—
287C42×C7—24no—
288C42×C7C2×D412yes—
289C42×C7C2412yes—
290C22×#41—21no—
291C22×SD16C22×C711yescharacteristic
292C22×M16C22×C711yescharacteristic
293C23×C8C22×C711yescharacteristic
294#552—24no—
295#552C22×C718yescomplemented
296#547—24no—
297#547C22×C718yes—
298C2×C4⋊Q8C22×C711yescharacteristic
299C2×#126—21no—
300C2×#125—21no—
301C2×#125C22×C711yescharacteristic
302C2×#123—21no—
303C2×#123—21no—
304C2×#123—21no—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8C22×C711yescharacteristic
307C2×C22⋊Q8C22×C711yescharacteristic
308C2×#121C22×C711yescharacteristic
309C2×#121C22×C711yescharacteristic
310C2×C4×Q8C22×C711yescharacteristic
311C2×C4×D4C22×C711yescharacteristic
312C2×C4×D4C22×C711yescharacteristic
313C2×#117—21no—
314C2×#117C22×C711yescharacteristic
315C22×C4⋊C4C22×C711yescharacteristic
316C22×C4⋊C4C22×C711yescharacteristic
317C22×C4⋊C4C22×C711yescharacteristic
318#501C22×C718yescomplemented
319#484C22×C718yescomplemented
320#483C22×C718yescomplemented
321#482C22×C718yescomplemented
322#480C22×C718yescomplemented
323#478C22×C718yescomplemented
324#477C22×C718yescomplemented
325#468C22×C718yescomplemented
326#465C22×C718yescomplemented
327#440C22×C718yescomplemented
328#435C22×C718yescomplemented
329#428C22×C718yescomplemented
330C2×#107C22×C711yescharacteristic
331C2×#107C22×C711yescharacteristic
332C2×#107C22×C711yescharacteristic
333C2×#107C22×C711yescharacteristic
334C2×#107C22×C711yescharacteristic
335C2×#107C22×C711yescharacteristic
336C2×#107C22×C718yescomplemented
337C2×#106C22×C711yescharacteristic
338C2×#106C22×C711yescharacteristic
339C2×#106C22×C711yescharacteristic
340C2×C4⋊C8C22×C711yescharacteristic
341C2×#103C22×C711yescharacteristic
342C2×#103C22×C711yescharacteristic
343C2×#103C22×C711yescharacteristic
344C2×#102C22×C711yescharacteristic
345C2×#102C22×C711yescharacteristic
346C2×#102C22×C711yescharacteristic
347C2×C22⋊C8C22×C711yescharacteristic
348C2×C22⋊C8C22×C711yescharacteristic
349C2×#97C22×C711yescharacteristic
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—42no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7AGL(1,ℤ/8)14yes—
360C23×C7C22×D412yes—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—48no—
366C7×Q8—42no—
367C7×D4—28no—
368C7×D4—22no—
369C7×D4—22no—
370C7×D4—48no—
371C7×D4—48no—
372C7×D4—42no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—24no—
378C2×C4×C7—24no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—48no—
391C2×C4×C7—48no—
392C2×C4×C7—42no—
393C2×C4×C7—48no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—42no—
397C2×C4×C7—42no—
398C2×C4×C7—42no—
399C2×C4×C7—48no—
400C2×C4×C7—42no—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D412yes—
404C2×C4×C7C22×D412yes—
405C2×C4×C7C22×D411yescharacteristic
406C2×C4×C7C2×#4112yes—
407C2×C4×C72−1+412yes—
408C2×C4×C7C2511yescharacteristic
409C7×C8—22no—
410C7×C8—22no—
411C7×C8—22no—
412C7×C8C2×#4114yescomplemented
413C2×#41—28no—
414C2×#41—48no—
415C22×Q8—21no—
416C22×Q8C23×C711yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C7×D411yescharacteristic
420C22×D4C23×C711yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C711yescharacteristic
426C23×C4C23×C711yescharacteristic
427C2×SD16—24no—
428C2×SD16C23×C714yes—
429C2×M16—24no—
430C2×M16C23×C714yes—
431C22×C8—24no—
432C22×C8C23×C711yescharacteristic
433C22×C8C23×C714yes—
434C22×C8C23×C711yescharacteristic
435C22×C8C23×C711yescharacteristic
436C22×C8C23×C711yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8C23×C714yes—
439#126—28no—
440#125—28no—
441#125—22no—
442#125C23×C714yes—
443#123—28no—
444#123—28no—
445#123—28no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—28no—
449C22⋊Q8C23×C714yes—
450C22⋊Q8C23×C714yes—
451#121—22no—
452#121—22no—
453#121C23×C714yes—
454#121C23×C714yes—
455C4×Q8—22no—
456C4×Q8C23×C714yes—
457C4×D4—22no—
458C4×D4C7×D414yes—
459C4×D4C23×C714yes—
460C4×D4C23×C714yes—
461#117—22no—
462#117—28no—
463#117C23×C714yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4C7×D411yescharacteristic
477C2×C4⋊C4C23×C711yescharacteristic
478C2×C4⋊C4C23×C711yescharacteristic
479C2×C4⋊C4C23×C711yescharacteristic
480C2×C4⋊C4C23×C711yescharacteristic
481C2×C4⋊C4C23×C711yescharacteristic
482C2×C4⋊C4C23×C714yes—
483C2×C4⋊C4C23×C714yes—
484C2×C4⋊C4C23×C714yes—
485C2×C4⋊C4C23×C711yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4C7×D411yescharacteristic
493C2×C22⋊C4C7×D411yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42C23×C711yescharacteristic
497#107C23×C714yes—
498#107C23×C714yes—
499#107C23×C714yes—
500#107C23×C714yes—
501#107C23×C714yes—
502#107C23×C714yes—
503#106C23×C714yes—
504#106C23×C714yes—
505#106C23×C714yes—
506C4⋊C8C23×C714yes—
507#103C23×C714yes—
508#103C23×C714yes—
509#103C23×C714yes—
510#102C23×C714yes—
511#102C23×C714yes—
512#102C23×C714yes—
513C22⋊C8C23×C714yes—
514C22⋊C8C23×C714yes—
515#97C23×C714yes—
516C22×C7—28no—
517C22×C7—22no—
518C22×C7—22no—
519C22×C7—22no—
520C22×C7—22no—
521C22×C7—22no—
522C22×C7—44no—
523C22×C7—42no—
524C22×C7—42no—
525C22×C7—42no—
526C22×C7—84no—
527C22×C7#54712yes—
528C22×C7C2×AGL(1,ℤ/8)14yes—
529C22×C7C2×AGL(1,ℤ/8)12yes—
530C22×C7#57812yes—
531C22×C7C23×D411yescharacteristic
532C4×C7—22no—
533C4×C7—22no—
534C4×C7—22no—
535C4×C7—22no—
536C4×C7—42no—
537C4×C7—42no—
538C4×C7—42no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7—42no—
543C4×C7#54712yes—
544C4×C7C22×#4111yescharacteristic
545C4×C7C2×2−1+411yescharacteristic
546C24—21no—
547C24C2×C7×D411yescharacteristic
548C24C2×C7×D411yescharacteristic
549#41—432no—
550C2×Q8—21no—
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—44no—
555C2×Q8C24×C712yes—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—44no—
563C2×D4—44no—
564C2×D4C2×C7×D414yes—
565C2×D4C24×C712yes—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4C2×C7×D411yescharacteristic
586C22×C4C2×C7×D411yescharacteristic
587C22×C4C2×C7×D411yescharacteristic
588C22×C4C2×C7×D411yescharacteristic
589C22×C4C2×C7×D412yes—
590C22×C4C2×C7×D412yes—
591C22×C4C24×C712yes—
592C22×C4C24×C712yes—
593C22×C4C24×C711yescharacteristic
594SD16—28no—
595M16—28no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—28no—
600C2×C8C7×#4114yescomplemented
601C2×C8C24×C712yes—
602C2×C8C24×C712yes—
603C2×C8C24×C712yes—
604C2×C8C24×C712yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4C2×C7×D414yes—
621C4⋊C4C24×C712yes—
622C4⋊C4C24×C712yes—
623C4⋊C4C24×C712yes—
624C4⋊C4C24×C712yes—
625C4⋊C4C24×C712yes—
626C4⋊C4C24×C712yes—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4C2×C7×D414yes—
634C22⋊C4C2×C7×D414yes—
635C42—24no—
636C42—24no—
637C42C2×C7×D412yes—
638C42C24×C712yes—
639C2×C7—24no—
640C2×C7—42no—
641C2×C7—82no—
642C2×C7#334314yesdirect product factor
643C2×C7C2×#54711yescharacteristic
644C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
645C2×C7C2×#57811yescharacteristic
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C7×AGL(1,ℤ/8)14yes—
656C23C22×C7×D412yes—
657C23C22×C7×D412yes—
658C23C22×C7×D411yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—48no—
662Q8—42no—
663D4—28no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—48no—
668D4—42no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—42no—
689C2×C4—48no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4C22×C7×D412yes—
698C2×C4C22×C7×D412yes—
699C2×C4C22×C7×D412yes—
700C2×C4C22×C7×D412yes—
701C2×C4C22×C7×D411yescharacteristic
702C2×C4C2×C7×#4112yes—
703C2×C4C7×2−1+412yes—
704C2×C4C25×C711yescharacteristic
705C8—22no—
706C8—22no—
707C8—22no—
708C8C2×C7×#4114yescomplemented
709C7C2×#334311yescharacteristic, direct product factor, Sylow
710C22—22no—
711C22—22no—
712C22—28no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22C7×#54712yes—
722C22C2×C7×AGL(1,ℤ/8)14yes—
723C22C2×C7×AGL(1,ℤ/8)12yes—
724C22C7×#57812yes—
725C22C23×C7×D411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4C7×#54712yes—
738C4C22×C7×#4111yescharacteristic
739C4C2×C7×2−1+411yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2C7×#334314yesdirect product factor
744C2C2×C7×#54711yescharacteristic
745C2C22×C7×AGL(1,ℤ/8)11yescharacteristic
746C2C2×C7×#57811yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#547C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#552C2semidirect
3. C7×#3343C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#484C2semidirect
6. C2×C7×#482C2semidirect
7. C2×C7×#483C2semidirect
8. C2×C7×#480C2semidirect
9. C2×C7×#477C2semidirect
10. C2×C7×#478C2semidirect
11. C2×C7×#468C2semidirect
12. C2×C7×#465C2semidirect
13. C2×C7×#440C2semidirect
14. C2×C7×#435C2semidirect
15. C2×C7×#428C2semidirect
16. C22×C7×#107C2semidirect
22. C7×#552C22semidirect
45. C7×#501C22semidirect
46. C7×#484C22semidirect
47. C7×#483C22semidirect
48. C7×#482C22semidirect
49. C7×#480C22semidirect
50. C7×#478C22semidirect
51. C7×#477C22semidirect
52. C7×#468C22semidirect
53. C7×#465C22semidirect
54. C7×#440C22semidirect
55. C7×#435C22semidirect
56. C7×#428C22semidirect
63. C2×C7×#107C22semidirect
77. C2×#3343C7direct (N × H)
181. C2×#552C2×C7semidirect
183. #3343C2×C7direct (N × H)
184. C2×#501C2×C7semidirect
185. C2×#484C2×C7semidirect
186. C2×#482C2×C7semidirect
187. C2×#483C2×C7semidirect
188. C2×#480C2×C7semidirect
189. C2×#477C2×C7semidirect
190. C2×#478C2×C7semidirect
191. C2×#468C2×C7semidirect
192. C2×#465C2×C7semidirect
193. C2×#440C2×C7semidirect
194. C2×#435C2×C7semidirect
195. C2×#428C2×C7semidirect
196. C22×#107C2×C7semidirect
251. C2×C7×C8#41semidirect
295. #552C22×C7semidirect
318. #501C22×C7semidirect
319. #484C22×C7semidirect
320. #483C22×C7semidirect
321. #482C22×C7semidirect
322. #480C22×C7semidirect
323. #478C22×C7semidirect
324. #477C22×C7semidirect
325. #468C22×C7semidirect
326. #465C22×C7semidirect
327. #440C22×C7semidirect
328. #435C22×C7semidirect
329. #428C22×C7semidirect
336. C2×#107C22×C7semidirect
412. C7×C8C2×#41semidirect
600. C2×C8C7×#41semidirect
642. C2×C7#3343direct (N × H)
708. C8C2×C7×#41semidirect
709. C7C2×#3343direct (N × H)
743. C2C7×#3343direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5522
C2×C7×#5472
C7×#33432
C2×C7×#5012
C2×C7×#4842
C2×C7×#4822
C2×C7×#4832
C2×C7×#4802
C2×C7×#4772
C2×C7×#4782
C2×C7×#4682
C2×C7×#4652
C2×C7×#4402
C2×C7×#4352
C2×C7×#4282
C22×C7×#1072
C2×#33437