Finite Group Databasebeta

← C2×C7×#3244 #13238074

Subgroups — C2×C7×#3244 #13238074

Order 1792.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic, complemented
2C2×C7×#542C211yesmaximal, characteristic
3C7×#3244C2116yesmaximal, direct product factor
4C2×C7×#501C211yesmaximal, characteristic, complemented
5C2×C7×#498C211yesmaximal, characteristic, complemented
6C2×C7×#489C211yesmaximal, characteristic, complemented
7C2×C7×#488C211yesmaximal, characteristic, complemented
8C2×C7×#481C211yesmaximal, characteristic
9C2×C7×#485C211yesmaximal, characteristic, complemented
10C2×C7×#482C211yesmaximal, characteristic
11C2×C7×#483C211yesmaximal, characteristic, complemented
12C2×C7×#479C211yesmaximal, characteristic, complemented
13C2×C7×#475C211yesmaximal, characteristic, complemented
14C2×C7×#478C211yesmaximal, characteristic, complemented
15C2×C7×#476C211yesmaximal, characteristic, complemented
16C2×C7×#433C211yesmaximal, characteristic, complemented
17C7×#544—24no—
18C7×#544C2218yescomplemented
19C7×#542—24no—
20C7×#542C2218yes—
21C2×C7×C4⋊Q8—21no—
22C2×C7×C4⋊Q8C2211yescharacteristic
23C2×C7×C4⋊Q8C2211yescharacteristic
24C2×C7×C4⋊Q8C2211yescharacteristic
25C2×C7×#126—21no—
26C2×C7×#125—21no—
27C2×C7×#125C2211yescharacteristic
28C2×C7×#125C2211yescharacteristic
29C2×C7×#124—21no—
30C2×C7×#124C2211yescharacteristic
31C2×C7×#123—21no—
32C2×C7×C22⋊Q8—21no—
33C2×C7×C22⋊Q8—21no—
34C2×C7×C22⋊Q8—21no—
35C2×C7×C22⋊Q8C2211yescharacteristic
36C2×C7×#121C2211yescharacteristic
37C2×C4×C7×Q8C2211yescharacteristic
38C2×C4×C7×D4C2211yescharacteristic
39C2×C7×#117C2211yescharacteristic
40C2×C7×#117C2211yescharacteristic
41C22×C7×C4⋊C4C2211yescharacteristic
42C7×#501C2218yescomplemented
43C7×#498C2218yescomplemented
44C7×#489C2218yescomplemented
45C7×#488C2218yescomplemented
46C7×#485C2218yescomplemented
47C7×#483C2218yescomplemented
48C7×#482C2218yes—
49C7×#481C2218yes—
50C7×#479C2218yescomplemented
51C7×#478C2218yescomplemented
52C7×#476C2218yescomplemented
53C7×#475C2218yescomplemented
54C7×#433C2218yescomplemented
55C2×C7×#107C2211yescharacteristic
56C2×C7×#107C2211yescharacteristic
57C2×C7×#106C2211yescharacteristic
58C2×C7×#106C2211yescharacteristic
59C2×C7×#106C2211yescharacteristic
60C2×C7×#106C2211yescharacteristic
61C2×C7×#106C2211yescharacteristic
62C2×C7×#106C2211yescharacteristic
63C2×C7×C4⋊C8C2211yescharacteristic
64C2×C7×C4⋊C8C2211yescharacteristic
65C2×C7×#103C2211yescharacteristic
66C2×C7×#103C2211yescharacteristic
67C2×C7×#103C2211yescharacteristic
68C2×C7×#103C2211yescharacteristic
69C2×C7×#102C2211yescharacteristic
70C2×C7×#102C2211yescharacteristic
71C2×C7×#102C2211yescharacteristic
72C2×C7×#102C2211yescharacteristic
73C2×C7×C22⋊C8C2211yescharacteristic
74C2×C7×C22⋊C8C2211yescharacteristic
75C2×C7×#97C2211yescharacteristic
76C2×C4×C7×C8C2211yescharacteristic
77C2×#3244C711yesmaximal, characteristic, direct product factor, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C22×C7×Q8—21no—
81C22×C7×Q8C2311yescharacteristic
82C22×C7×D4—21no—
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C22×C7×C8C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C22×C7×C8C2311yescharacteristic
91C7×C4⋊Q8—28no—
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8—22no—
94C7×C4⋊Q8—22no—
95C7×C4⋊Q8C2314yes—
96C7×C4⋊Q8C2314yes—
97C7×C4⋊Q8C2314yes—
98C7×#126—28no—
99C7×#125—28no—
100C7×#125—22no—
101C7×#125—22no—
102C7×#125C2314yes—
103C7×#125C2314yes—
104C7×#124—28no—
105C7×#124—22no—
106C7×#124C2314yes—
107C7×#123—28no—
108C7×C22⋊Q8—22no—
109C7×C22⋊Q8—28no—
110C7×C22⋊Q8—28no—
111C7×C22⋊Q8—28no—
112C7×C22⋊Q8C2314yes—
113C7×#121—22no—
114C7×#121C2314yes—
115C4×C7×Q8—22no—
116C4×C7×Q8C2314yes—
117C4×C7×D4—22no—
118C4×C7×D4C2314yes—
119C7×#117—22no—
120C7×#117D414yes—
121C7×#117C2314yes—
122C7×#117C2314yes—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—22no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—21no—
127C2×C7×C4⋊C4—21no—
128C2×C7×C4⋊C4—21no—
129C2×C7×C4⋊C4—21no—
130C2×C7×C4⋊C4—21no—
131C2×C7×C4⋊C4—21no—
132C2×C7×C4⋊C4—21no—
133C2×C7×C4⋊C4—21no—
134C2×C7×C4⋊C4D411yescharacteristic
135C2×C7×C4⋊C4D411yescharacteristic
136C2×C7×C4⋊C4C2314yes—
137C2×C7×C4⋊C4C2311yescharacteristic
138C2×C7×C4⋊C4C2311yescharacteristic
139C2×C7×C4⋊C4C2311yescharacteristic
140C2×C7×C4⋊C4C2311yescharacteristic
141C2×C7×C4⋊C4C2311yescharacteristic
142C2×C7×C4⋊C4C2311yescharacteristic
143C2×C7×C22⋊C4—21no—
144C2×C7×C22⋊C4—21no—
145C2×C7×C22⋊C4—21no—
146C2×C7×C22⋊C4—21no—
147C2×C7×C22⋊C4—21no—
148C2×C7×C22⋊C4—21no—
149C2×C7×C22⋊C4D411yescharacteristic
150C2×C7×C22⋊C4D411yescharacteristic
151C2×C42×C7—21no—
152C2×C42×C7—21no—
153C2×C42×C7C2311yescharacteristic
154C2×C42×C7C2311yescharacteristic
155C7×#107C2314yes—
156C7×#107C2314yes—
157C7×#106C2314yes—
158C7×#106C2314yes—
159C7×#106C2314yes—
160C7×#106C2314yes—
161C7×#106C2314yes—
162C7×#106C2314yes—
163C7×C4⋊C8C2314yes—
164C7×C4⋊C8C2314yes—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173C7×C22⋊C8C2314yes—
174C7×C22⋊C8C2314yes—
175C7×#97C2314yes—
176C4×C7×C8C2314yes—
177C2×#544C2×C711yescharacteristic, complemented
178C2×#542C2×C711yescharacteristic
179#3244C2×C7116yesdirect product factor
180C2×#501C2×C711yescharacteristic, complemented
181C2×#498C2×C711yescharacteristic, complemented
182C2×#489C2×C711yescharacteristic, complemented
183C2×#488C2×C711yescharacteristic, complemented
184C2×#481C2×C711yescharacteristic
185C2×#485C2×C711yescharacteristic, complemented
186C2×#482C2×C711yescharacteristic
187C2×#483C2×C711yescharacteristic, complemented
188C2×#479C2×C711yescharacteristic, complemented
189C2×#475C2×C711yescharacteristic, complemented
190C2×#478C2×C711yescharacteristic, complemented
191C2×#476C2×C711yescharacteristic, complemented
192C2×#433C2×C711yescharacteristic, complemented
193C24×C7—21no—
194C24×C7C2×D411yescharacteristic
195C2×C7×Q8—21no—
196C2×C7×Q8—24no—
197C2×C7×Q8—24no—
198C2×C7×Q8—24no—
199C2×C7×Q8—22no—
200C2×C7×Q8—22no—
201C2×C7×Q8—82no—
202C2×C7×Q8—82no—
203C2×C7×Q8—82no—
204C2×C7×Q8C2412yes—
205C2×C7×D4—24no—
206C2×C7×D4—21no—
207C2×C7×D4—22no—
208C2×C7×D4—22no—
209C2×C7×D4—82no—
210C2×C7×D4C2412yes—
211C22×C4×C7—22no—
212C22×C4×C7—22no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—24no—
222C22×C4×C7—82no—
223C22×C4×C7—82no—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2412yes—
231C22×C4×C7C2411yescharacteristic
232C2×C7×C8—22no—
233C2×C7×C8—22no—
234C2×C7×C8—22no—
235C2×C7×C8—22no—
236C2×C7×C8C2412yes—
237C2×C7×C8C2412yes—
238C2×C7×C8C2412yes—
239C2×C7×C8C2412yes—
240C7×C4⋊C4—24no—
241C7×C4⋊C4—21no—
242C7×C4⋊C4—21no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—21no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4C2×D414yes—
257C7×C4⋊C4C2×D414yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C7×C4⋊C4C2412yes—
263C7×C4⋊C4C2412yes—
264C7×C22⋊C4—24no—
265C7×C22⋊C4—24no—
266C7×C22⋊C4—24no—
267C7×C22⋊C4—24no—
268C7×C22⋊C4—24no—
269C7×C22⋊C4—24no—
270C7×C22⋊C4C2×D414yes—
271C7×C22⋊C4C2×D414yes—
272C42×C7—24no—
273C42×C7—24no—
274C42×C7C2×D412yes—
275C42×C7C2×D412yes—
276C42×C7C2412yes—
277C42×C7C2412yes—
278#544—24no—
279#544C22×C718yescomplemented
280#542—24no—
281#542C22×C718yes—
282C2×C4⋊Q8—21no—
283C2×C4⋊Q8C22×C711yescharacteristic
284C2×C4⋊Q8C22×C711yescharacteristic
285C2×C4⋊Q8C22×C711yescharacteristic
286C2×#126—21no—
287C2×#125—21no—
288C2×#125C22×C711yescharacteristic
289C2×#125C22×C711yescharacteristic
290C2×#124—21no—
291C2×#124C22×C711yescharacteristic
292C2×#123—21no—
293C2×C22⋊Q8—21no—
294C2×C22⋊Q8—21no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8C22×C711yescharacteristic
297C2×#121C22×C711yescharacteristic
298C2×C4×Q8C22×C711yescharacteristic
299C2×C4×D4C22×C711yescharacteristic
300C2×#117C22×C711yescharacteristic
301C2×#117C22×C711yescharacteristic
302C22×C4⋊C4C22×C711yescharacteristic
303#501C22×C718yescomplemented
304#498C22×C718yescomplemented
305#489C22×C718yescomplemented
306#488C22×C718yescomplemented
307#485C22×C718yescomplemented
308#483C22×C718yescomplemented
309#482C22×C718yes—
310#481C22×C718yes—
311#479C22×C718yescomplemented
312#478C22×C718yescomplemented
313#476C22×C718yescomplemented
314#475C22×C718yescomplemented
315#433C22×C718yescomplemented
316C2×#107C22×C711yescharacteristic
317C2×#107C22×C711yescharacteristic
318C2×#106C22×C711yescharacteristic
319C2×#106C22×C711yescharacteristic
320C2×#106C22×C711yescharacteristic
321C2×#106C22×C711yescharacteristic
322C2×#106C22×C711yescharacteristic
323C2×#106C22×C711yescharacteristic
324C2×C4⋊C8C22×C711yescharacteristic
325C2×C4⋊C8C22×C711yescharacteristic
326C2×#103C22×C711yescharacteristic
327C2×#103C22×C711yescharacteristic
328C2×#103C22×C711yescharacteristic
329C2×#103C22×C711yescharacteristic
330C2×#102C22×C711yescharacteristic
331C2×#102C22×C711yescharacteristic
332C2×#102C22×C711yescharacteristic
333C2×#102C22×C711yescharacteristic
334C2×C22⋊C8C22×C711yescharacteristic
335C2×C22⋊C8C22×C711yescharacteristic
336C2×#97C22×C711yescharacteristic
337C2×C4×C8C22×C711yescharacteristic
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
342C23×C7—42no—
343C23×C7—42no—
344C23×C7—42no—
345C23×C7C22×D412yes—
346C23×C7C22×D411yescharacteristic
347C7×Q8—22no—
348C7×Q8—22no—
349C7×Q8—42no—
350C7×Q8—84no—
351C7×Q8—84no—
352C7×Q8—84no—
353C7×D4—22no—
354C7×D4—22no—
355C7×D4—42no—
356C7×D4—84no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7—42no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—84no—
380C2×C4×C7—84no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D411yescharacteristic
387C2×C4×C72−1+412yes—
388C2×C4×C72−1+412yes—
389C2×C4×C7C2511yescharacteristic
390C7×C8—22no—
391C7×C8—22no—
392C7×C8—22no—
393C7×C8—22no—
394C22×Q8—21no—
395C22×Q8—21no—
396C22×Q8—21no—
397C22×Q8C23×C711yescharacteristic
398C22×D4—21no—
399C22×D4C23×C711yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C711yescharacteristic
403C22×C8C23×C711yescharacteristic
404C22×C8C23×C711yescharacteristic
405C22×C8C23×C711yescharacteristic
406C22×C8C23×C711yescharacteristic
407C4⋊Q8—28no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410C4⋊Q8—22no—
411C4⋊Q8C23×C714yes—
412C4⋊Q8C23×C714yes—
413C4⋊Q8C23×C714yes—
414#126—28no—
415#125—28no—
416#125—22no—
417#125—22no—
418#125C23×C714yes—
419#125C23×C714yes—
420#124—28no—
421#124—22no—
422#124C23×C714yes—
423#123—28no—
424C22⋊Q8—22no—
425C22⋊Q8—28no—
426C22⋊Q8—28no—
427C22⋊Q8—28no—
428C22⋊Q8C23×C714yes—
429#121—22no—
430#121C23×C714yes—
431C4×Q8—22no—
432C4×Q8C23×C714yes—
433C4×D4—22no—
434C4×D4C23×C714yes—
435#117—22no—
436#117C7×D414yes—
437#117C23×C714yes—
438#117C23×C714yes—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C7×D411yescharacteristic
451C2×C4⋊C4C7×D411yescharacteristic
452C2×C4⋊C4C23×C711yescharacteristic
453C2×C4⋊C4C23×C711yescharacteristic
454C2×C4⋊C4C23×C714yes—
455C2×C4⋊C4C23×C711yescharacteristic
456C2×C4⋊C4C23×C711yescharacteristic
457C2×C4⋊C4C23×C711yescharacteristic
458C2×C4⋊C4C23×C711yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4C7×D411yescharacteristic
466C2×C22⋊C4C7×D411yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C711yescharacteristic
470C2×C42C23×C711yescharacteristic
471#107C23×C714yes—
472#107C23×C714yes—
473#106C23×C714yes—
474#106C23×C714yes—
475#106C23×C714yes—
476#106C23×C714yes—
477#106C23×C714yes—
478#106C23×C714yes—
479C4⋊C8C23×C714yes—
480C4⋊C8C23×C714yes—
481#103C23×C714yes—
482#103C23×C714yes—
483#103C23×C714yes—
484#103C23×C714yes—
485#102C23×C714yes—
486#102C23×C714yes—
487#102C23×C714yes—
488#102C23×C714yes—
489C22⋊C8C23×C714yes—
490C22⋊C8C23×C714yes—
491#97C23×C714yes—
492C4×C8C23×C714yes—
493C22×C7—22no—
494C22×C7—22no—
495C22×C7—22no—
496C22×C7—44no—
497C22×C7—42no—
498C22×C7—42no—
499C22×C7—42no—
500C22×C7—84no—
501C22×C7#53612yes—
502C22×C7#57712yes—
503C22×C7#57712yes—
504C22×C7C23×D411yescharacteristic
505C4×C7—22no—
506C4×C7—22no—
507C4×C7—22no—
508C4×C7—22no—
509C4×C7—22no—
510C4×C7—42no—
511C4×C7—42no—
512C4×C7—42no—
513C4×C7—42no—
514C4×C7—42no—
515C4×C7—42no—
516C4×C7—42no—
517C4×C7#53612yes—
518C4×C7C2×2−1+411yescharacteristic
519C4×C7C2×2−1+411yescharacteristic
520C24—21no—
521C24C2×C7×D411yescharacteristic
522C2×Q8—21no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—82no—
529C2×Q8—82no—
530C2×Q8—82no—
531C2×Q8C24×C712yes—
532C2×D4—24no—
533C2×D4—21no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—82no—
537C2×D4C24×C712yes—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4C2×C7×D411yescharacteristic
552C22×C4C2×C7×D411yescharacteristic
553C22×C4C2×C7×D411yescharacteristic
554C22×C4C2×C7×D411yescharacteristic
555C22×C4C2×C7×D411yescharacteristic
556C22×C4C2×C7×D412yes—
557C22×C4C24×C712yes—
558C22×C4C24×C711yescharacteristic
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8C24×C712yes—
564C2×C8C24×C712yes—
565C2×C8C24×C712yes—
566C2×C8C24×C712yes—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4C2×C7×D414yes—
584C4⋊C4C2×C7×D414yes—
585C4⋊C4C24×C712yes—
586C4⋊C4C24×C712yes—
587C4⋊C4C24×C712yes—
588C4⋊C4C24×C712yes—
589C4⋊C4C24×C712yes—
590C4⋊C4C24×C712yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4C2×C7×D414yes—
598C22⋊C4C2×C7×D414yes—
599C42—24no—
600C42—24no—
601C42C2×C7×D412yes—
602C42C2×C7×D412yes—
603C42C24×C712yes—
604C42C24×C712yes—
605C2×C7—42no—
606C2×C7—82no—
607C2×C7#324414yesdirect product factor
608C2×C7C2×#53611yescharacteristic
609C2×C7C2×#57711yescharacteristic
610C2×C7C2×#57711yescharacteristic
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23C22×C7×D412yes—
619C23C22×C7×D411yescharacteristic
620Q8—22no—
621Q8—22no—
622Q8—42no—
623Q8—84no—
624Q8—84no—
625Q8—84no—
626D4—22no—
627D4—22no—
628D4—42no—
629D4—84no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—84no—
653C2×C4—84no—
654C2×C4C22×C7×D412yes—
655C2×C4C22×C7×D412yes—
656C2×C4C22×C7×D412yes—
657C2×C4C22×C7×D412yes—
658C2×C4C22×C7×D412yes—
659C2×C4C22×C7×D411yescharacteristic
660C2×C4C7×2−1+412yes—
661C2×C4C7×2−1+412yes—
662C2×C4C25×C711yescharacteristic
663C8—22no—
664C8—22no—
665C8—22no—
666C8—22no—
667C7C2×#324411yescharacteristic, direct product factor, Sylow
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22C7×#53612yes—
677C22C7×#57712yes—
678C22C7×#57712yes—
679C22C23×C7×D411yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4C7×#53612yes—
693C4C2×C7×2−1+411yescharacteristic
694C4C2×C7×2−1+411yescharacteristic
695C2—42no—
696C2—82no—
697C2C7×#324414yesdirect product factor
698C2C2×C7×#53611yescharacteristic
699C2C2×C7×#57711yescharacteristic
700C2C2×C7×#57711yescharacteristic
subgroupG/H
center, socleC23×C7C22×D4
commutator, Frattini, cosocleC2×C4C25×C7
prime radicalC2×C7×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C7×#544C2semidirect
3. C7×#3244C2direct (N × H)
4. C2×C7×#501C2semidirect
5. C2×C7×#498C2semidirect
6. C2×C7×#489C2semidirect
7. C2×C7×#488C2semidirect
9. C2×C7×#485C2semidirect
11. C2×C7×#483C2semidirect
12. C2×C7×#479C2semidirect
13. C2×C7×#475C2semidirect
14. C2×C7×#478C2semidirect
15. C2×C7×#476C2semidirect
16. C2×C7×#433C2semidirect
18. C7×#544C22semidirect
42. C7×#501C22semidirect
43. C7×#498C22semidirect
44. C7×#489C22semidirect
45. C7×#488C22semidirect
46. C7×#485C22semidirect
47. C7×#483C22semidirect
50. C7×#479C22semidirect
51. C7×#478C22semidirect
52. C7×#476C22semidirect
53. C7×#475C22semidirect
54. C7×#433C22semidirect
77. C2×#3244C7direct (N × H)
177. C2×#544C2×C7semidirect
179. #3244C2×C7direct (N × H)
180. C2×#501C2×C7semidirect
181. C2×#498C2×C7semidirect
182. C2×#489C2×C7semidirect
183. C2×#488C2×C7semidirect
185. C2×#485C2×C7semidirect
187. C2×#483C2×C7semidirect
188. C2×#479C2×C7semidirect
189. C2×#475C2×C7semidirect
190. C2×#478C2×C7semidirect
191. C2×#476C2×C7semidirect
192. C2×#433C2×C7semidirect
279. #544C22×C7semidirect
303. #501C22×C7semidirect
304. #498C22×C7semidirect
305. #489C22×C7semidirect
306. #488C22×C7semidirect
307. #485C22×C7semidirect
308. #483C22×C7semidirect
311. #479C22×C7semidirect
312. #478C22×C7semidirect
313. #476C22×C7semidirect
314. #475C22×C7semidirect
315. #433C22×C7semidirect
607. C2×C7#3244direct (N × H)
667. C7C2×#3244direct (N × H)
697. C2C7×#3244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5442
C2×C7×#5422
C7×#32442
C2×C7×#5012
C2×C7×#4982
C2×C7×#4892
C2×C7×#4882
C2×C7×#4812
C2×C7×#4852
C2×C7×#4822
C2×C7×#4832
C2×C7×#4792
C2×C7×#4752
C2×C7×#4782
C2×C7×#4762
C2×C7×#4332
C2×#32447